Semester-I

1.1. Mechanics1

Motion of a particle in one dimension: Newtons second law. Momentum, impulse, kinetic energy, theenergy theorem, work and power. Conservation of linear momentum. The motion of a rocket ejecting fuel.Conservative force depending on position. Potential energy. Conservation of energy. Example of the motionunder the restoring force F = kx.Vector Kinematics: The Cartesian basis vectors {i, j, k} and their properties. Cartesian componentsof a vector. The vector function A(t) of a single variable t and its derivative (dA/dt). The derivatives(d/dt)(A+ B), (d/dt)(A B), and (d/dt)(AB) where and are scalar functions and A and B arevector functions of t. The equation to the trajectory of a particle in the parametric form r = r(t). Thevelocity dr/dt of the particle as a tangent vector to its orbit r = r(t). The acceleration vector d2r/dt2.Calculation of the velocity and acceleration of a particle moving along

(1) the straight line r(t) = 12at2+bt+c where a, b, and c, are constants, and

(2) the circle r(t) = R (i cost + j sint), where R is a constant and = (t).

Newtons laws of motion in vector form. The equations of motion in Cartesian and plane polar co-ordinates.Radial and transverse components of velocity and acceleration.

Torque and angular momentum: The definition of the angular momentum and torque of a particle relativeto an origin. Newtons second law in the angular form (dL/dt) = rF. Conservation of angular momentumof a particle moving under a central force. Motion under an inverse square law of force. Derivation ofKeplers laws of planetary motion.

References

1. Mechanics, K.R.Simon, Addison-Wesley, Reading, Massachusetts, 1963, Chapters 2 and 3.2. Newtonian Mechanics, A.P.French, The English Language Book Society and Nelson, 1973, Chapter 13.3. Vector Mechanics, 2nd. Edn., D.E.Christie, McGraw-Hill, New York, 19644. Fundamentals of Physics, Extended 3rd. Edn., D.Halliday, R.Resnick and J.Merryl, John Wiley, New

York, 1988, Sections 11-9, 12-4, 12-5,12-6, 15-8, and 15-9.

1.2. Mathematics1

Functions and derivatives: Functions and graphs: Functions. Sums, differences, products and quotientsof functions. Graphs of functions. Monotone functions. Even and odd functions. Polynomials. Longdivision. Roots of polynomials. Types of functions. Continuous functions; examples. Definition of continuity.Intermediate value theorem. Inverse functions. Definition of limits; computing limits; examples. Derivatives:Definition of the derivative. Computing derivatives from the definition. The derivative as a new function.The Leibniz notation. The linear approximation theorem. Using the derivative to compute function values.Continuity of differentiable functions. Basic rules of differentiation; examples. The chain rule. Derivativesof inverse functions, power functions and radical functions. Non-differentiable functions. Higher derivatives.Differentiability assumptions in physics. Applications of the derivative: Tangent and normal lines; Increasingand decreasing functions; Extrema of functions. Increments and differentials of a function of one variable.(16 Hours)

Sequences and series: Elementary ideas of sequences, series, limits and convergence. Absolute convergence.Tests for convergence. Power series. Binomial series. Taylor and MacLaurin series and their application to

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the local approximation of a function by a polynomial and to finding limits.

Integration: The definite integral as the area under a curve. Analytic definition of the integral. Relationshipbetween the derivative and the integralthe fundamental theorem of calculus. Antiderivatives (Primitivefunctions). Indefinite integrals.

Formal integration: Basic rules; integration by parts; the language of differentials; changing variables; ele-mentary trigonometric, exponential and algebraic integrals; (Only simple cases need be discussed). Derivativeand integral of power series. Mention of the available computer packages such as Mathematica and MuPADfor doing calculus.

Vectors: Vector algebra; addition, subtraction, scalar multiplication and linear combinations of vectors.The centroid of a system of weighted points. The Scalar product of vectors and its properties. The Schwarzinequality: (A B)2 (A A)(B B). Vector products. Elementary vector geometry of lines and planes:Equations of a straight line; Distance of a point from a line. Distance between two lines. Equations for aplane; Distance from a point to a plane; Projections onto a plane.

References

1. Mathematical Methods in the Physical Sciences, M.L.Boas, 2nd. Edn., Wiley, New York, 19832. All you wanted to know about Mathematics but were afraid to ask: Mathematics for Science Students,

L.Lyons, Cambridge University Press, Cambridge, 19983. Calculus, Vols. 1 and 2, Lipman Bers, IBH Publishing Company, Bombay, 19734. Calculus with analytic geometry, R.E.Johnson and F.L.Kiokemeister, Allyn and Bacon, Boston, 19585. Vector Mechanics,2nd. Edn., D.E.Christie, McGraw-Hill, New York, 19646. Advanced Vector Analysis, C.E.Weatherburn, G.Bell and Sons, London, 19607. Vector Analysis, Louis Brand, Wiley International, Toppan Company, Tokyo, 19578. Vector Analysis and an Introduction to Tensor Analysis, (Schaums Outline Series) M.R.Spiegel, Tata

McGraw-Hill, New Delhi

1.3. Computer-basics, Arithmetic and Statistics

Introduction: Elements of computer processing; Hardware, CPU: Commonly used CPUs like ix86, 68x,Alpha, Sparc, MIPS, etc., VDU; I/O Devices; Storage Devices: Removable and Non-removable media, Com-monly used media like floppies, hard disks, CDs, tapes; Qualitative introduction about magnetic, magneto-optical and optical techniques; Operating systems: Overview, General introduction to Unix, Linux, MS-DOS,MS-Windows, etc.; Single and Multiuser systems. Software: Productivity applications: Text/Word proces-sors, Spreadsheets, Drawing programs, Graphing programs, Databases, Presentation programs; Developmentapplications: Assembly language; High-level languages: Pascal, C, C++, Fortran, Basic, perl, python, Tcl.Compilers and Interpreters (Qualitative introduction highlighting the salient features of the language).

Computer Arithmetic: Integers; Floating point representation of numbers; Arithmetic operations withnormalisation; Errors in representation; Commonly used number types and their limits like max. and min.integer, float, double precision, long, etc.

Description of Data: Introduction; Moments of a distribution: Mean; Variance; Skewness; Efficient searchfor the median; Estimation of the mode for continuous data; Two distributions: Students t-test, F -test,Chi-square test, t-test; 2-test; Linear correlation; Nonparametric or Rank correlation; Smoothing of data.

Modelling of data: Introduction; Least-squares as a maximum likelihood estimator; Fitting data to astraight line; General linear least squares; Nonlinear models; Confidence limits; Robust estimation.

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References

1. Fundamentals of computers, 3rd Edition, V.Rajaraman, Prentice-Hall of India, 19992. Computer oriented numerical methods, 3rd. Edn., V.Rajaraman, Prentice-Hall of India, 20003. Statistics, M.R.Spiegel, Schaum Series, Asian Student Edition4. Numerical recipes in C, W.H.Press, B.T.Flannery, S.A.Teukolsky, and Vetterling, Cambridge Univer-

sity Press, Cambridge, 1988

1.4. Acoustics

Wave motion: Physical characteristics of wave motion in one dimension: amplitude, phase, frequency,wavelength, wave number, wave vector and velocity. Superposition of two waves of different frequencies:beats. Elementary discussion of dispersive media; relations for phase and group velocities.

Vibrations of mechanical systems: Vibrations with damping and a forcing term, but restricted to onevariable other than time; resonance and Q-factor. Critical damping. Compound pendulum. Vibration ofrods, strings, membranes and strips. Longitudinal vibrations in a rod. Vibrations of a stretched string anda rectangular membranes. Harmonics. Qualitative discussion of the vibrations of a strip (of a rectangularcross-section); modes of vibration.

Analysis of sound waves: Fouriers theorem; the example of a square wave; superposition of simpleharmonic waves; Lissajous figures.

References

1. Vibration and waves in Physics, I.G.Main, 3rd. Edition, Cambridge University Press, Cambridge, 19932. Waves, (Berkeley Physics Course, Vol. III), Crawford, McGraw-Hill, New York3. Vibrations and waves, A.P.French, Chapman and Hall, London4. Acoustics, Kinsler and Frey5. Fundamentals of Physics, Extended 3rd. Edn., D.Halliday, R.Resnick and J.Merryl, John Wiley, New

York, 1988, Chapters 17 and 18.

1.5. Lab1: Computer Basics

Any eight of the following:

1. Familiarisation with computer internals2. Using Scilab/Octave3. Using Symbolic Algebra Package4. Using LATEX5. Using plotting programs (Gnuplot and/or Scigraphica)6. Using word processor7. Using spreadsheet8. Using drawing program9. Using presentation software

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Semester-II

2.1. Heat and Thermodynamics1

The zeroth and first laws of thermodynamics: Thermodynamic equilibrium, zeroth law. First law.Isothermal and adiabatic changes. Phase diagrams. Work done in isothermal and adiabatic changes. Heatcapacities. Equation of state for an ideal gas and simple non- ideal (van der Waals) gases.

Second law of thermodynamics: The Kelvin and Clausius statements of the second law. Heat engines.Carnot cycles and their reversibility. Efficiency of a Carnot engine. Carnot theorem. Absolute scale oftemperature. Equivalence to the ideal gas scale. Definition of entropy. Reversible and irreversible processesand associated changes in entropy.

Liquefaction of gases: Porous plug experiment. Temperature of inversion. Principle of regenerativecooling. Adiabatic demagnetisation. Concept of the absolute zero of temperature. Statement of the thirdlaw of thermodynamics.

Blackbody radiation: Distribution of energy in the blackbody spectrum. Statement of Wiens law andRayleigh-Jeans law. Derivation of Plancks law from Einstein A and B coefficients. Wien law and Rayleigh-Jeans law derived as limiting cases of the Planck law. The Wien displacement law. The Stefan law ofradiation, surface temperature of the sun.

References

1. Equilibrium Thermodynamics, C.Adkins, Cambridge University Press, Cambridge2. Modern Thermodynamics, D.K.Kondepudi and I.Prigogine, John-Wiley3. The Feynmann Lectures on Physics, Vol.II, R.P.Feynmann, R.B.Leighton and M.Sands, Chapters 44-

46, Addison-Wesley, Reading, Massachusetts.4. Fundamentals of Physics, Extended 3rd. Edn., D.Halliday, R.Resnick and J.Merryl, John Wiley, New

York, 1988, Chapters 19 to 22.5. University Physics, 4th. Edn., F.W.Sears and M.W.Zemansky, Addison-Wesley, Reading, Massachusetts,

1973, Chapters 15 to 20

2.2. Mathematics2

Differential calculus of functions of more than one variable: Functions of several variables. Partialderivatives. The chain rule. Implicit differentiation.

Functions of two variables: Two-variable functions as surfaces; geometric interpretation of the partialderivative; directional derivatives; line integrals. Taylor expansion for two variables, maxima, minima andsaddle points of functions of two variables. Lagrange multipliers for stationary points of functions of twovariables.

Analytic geometry of conic sections: Conic sections. Standard equations. Asymptotes, foci, directrices,eccentricity and tangents. Conics in polar coordinates. Parametric equations. Rotation of coordinate axesin the plane and the general equation of the second degree. Classification of conics through the generalequation.

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References

1. Mathematical Methods in the Physical Sciences, 2nd Edition, M.L.Boas, John Wiley, New York, 19832. All you wanted to know about Mathematics but were afraid to ask: Mathematics for Science Students,

L.Lyons, Cambridge University Press, Cambridge, 19983. Calculus, Vols. 1 and 2, Lipman Bers, IBH Publishing Company, Bombay, 19734. Calculus with analytic geometry, R.E.Johnson and F.L.Kiokemeister, Allyn and Bacon, Boston, 19585. Advanced Vector Analysis, C.E.Weatherburn, G.Bell and Sons, London, 19606. Vector Analysis and an Introduction to Tensor Analysis, (Schaums Outline Series) M.R.Spiegel, Tata

McGraw-Hill, New Delhi, 1973

2.3. Computer Applications

Introduction to Programming: Problem solving by computers; Flowcharts; Algorithms; Elements of pro-gramming; Brief introduction to object-oriented programming.

Programming in Pascal and C: Basics of program writing: Writing, Compiling and Running the pro-gram;Style: Common coding practices, Clarity, Simplicity, Commenting; Basic Declaration and Expressions;Arrays, Qualifiers and Reading numbers; Decision and Control statements: if, else statements, looping state-ments, while, break, continue, for, etc. statements; Variable scope and functions; Bit operations; Advancedtypes: structures, unions, enum type, arrays of structures, casting; Simple pointers: Pointers and functionarguments, Pointers and arrays, Pointers and structures; File Input/Output: Binary and ASCII files, Binaryand ASCII I/O, Designing file formats; Modular programming.

Programming in Python: Introduction; Simple Python statements; Control flow tools: if, for state-ments,range() function, break, continue and pass statements, defining functions; Data structures; Modules;Input/Output

References

1. Problem solving and programming in Pascal, M.G. Schneider, Wiley-Eastern, 19912. Practical C programming, 3rd Edition, S. Oualline, OReilly, 19973. Python: On-line documentation4. On-line docs for Pascal and C should also be referred.

2.4. Electronics1

Foundations: Voltage and current. Relation between voltage and current: resistors (colour code, resistorsin series and parallel, power in resistors, ratings) Voltage dividers. Voltage and current sources. Theveninsequivalent circuit. Small signal resistance - example of zener diode.

Signals: Sinusoidal signals. Signal amplitudes and decibels. Other signals (ramp, triangle, noise, squarewaves, pulses, steps and spikes). Logic levels. Signal sources (signal generators, pulse generators, functiongenerators).

Capacitors and ac circuits: Capacitors (The relations Q = CV and I = C(dV/dt), capacitors in paralleland series, capacitor colour codes and voltage ratings.) RC circuits. V and I versus time. Differentiators.Unintentional capacitive coupling. Integrators.

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Inductors and transformers: Inductors, transformers, impedance and reactance. Frequency analysis ofreactive circuits. Voltages and currents as complex numbers. Reactance of capacitors and inductors. Thegeneralised Ohm law. Power in a reactive circuit. Generalised voltage dividers.

RC Filters: Phasor diagrams. High pass filters, low pass filters, Poles and decibels per octave. Resonantcircuits and active filters. Other capacitor applications (bypassing, power supply filtering, timing and waveform generation). Generalised Thevenin theorem.

Diodes and Diode Circuits: Diodes. Rectification, Power supply filtering. Full wave bridge, center tappedfull wave rectifier, split supply, voltage multipliers. Regulators. Circuit application of diodes. Inductiveloading and diode protection.

Transistors: First transistor model - the current amplifier. Transistor switch. Emitter follower. Emitterfollowers as voltage regulators. Emitter follower biasing. Transistor current source. Common emitteramplifier. Unity-gain phase splitter. Transconductance.

Amplifier building blocks: Push-pull output stages. Darlington connection. Bootstrapping. Differentialamplifiers. Feedback voltage regulator.

References

1. The art of electronics: P. Horowitz and W. Hill, Second Edition, Cambridge University Press, 1995,pages 1-111.

2.5. Lab-2: Computer Applications

1. Programming in Pascal-12. Programming in Pascal-23. Programming in Pascal-34. Programming in C-15. Programming in C-26. Programming in C-37. Programming in Python-18. Programming in Python-2

Semester-III

3.1. Mechanics2

Frames of reference: Inertial frame. Galilean principle of relativity. Non-inertial frames. Centrifugal,Coriolis and other pseudo forces.

Systems of point particles: Center of mass frame and its uses. Moment of inertia of a system of particles.Use of perpendicular and parallel-axis theorems. Moment of inertia of simple bodies (the formula for anymoment of inertia will be given). Solution of simple dynamical problems involving rotations about a fixedaxis.

Special theory of relativity: The constancy of the speed of light. Simultaneity. The Lorentz transformation(derivation not required). Time dilation and length contraction. The addition of velocities. Invariance of the

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space-time interval. Energy, momentum, rest mass and their relationship for a single particle. Conservationof energy and momentum. Elementary kinematics of the scattering and decay of sub- atomic particles,including the photon.

References

1. Newtonian Mechanics, A.P.French (MIT Series), ELBS and Nelson,2. Introduction to Classical Mechanics, A.P.French and M.G.Ebison, Chapman and Hall, London3. Mechanics, C.Kittel, Knight and Ruderman, Berkely Physics Course, Vol.I, McGraw-Hill, New York4. Mechanics, K.R.Simon, Addison-Wesley, Reading, Massachusetts, 1963, Chapters 2 and 3.5. Vector Mechanics, 2nd. Edn., D.E.Christie, McGraw-Hill, New York, 19646. Fundamentals of Physics, Extended 3rd. Edn., D.Halliday, R.Resnick and J.Merryl, John Wiley, New

York, 19887. Special Relativity, A.P.French (MIT Series), ELBS and Nelson, 19728. Spacetime Physics, E.F.Taylor and J.A.Wheeler, W.H.Freeman and Company, San Francisco, 1966

3.2. Mathematics3

Complex algebra: Complex numbers, definitions and operators. The Argand diagram, modulus andargument (phase) and their geometric interpretation; curves in the Argand diagram. De Moivres theoremand its application to evaluation of the roots of unity, to the solution of polynomial equations and to thesummation of series of sines and cosines. Elementary functions (polynomial, trigonometric, exponential,hyperbolic, logarithmic) of a complex variable.

Matrices and determinants: Linearity and its importance in physics. Matrices. Elementary properties (ad-dition, multiplication, inverse) of two and three dimensional matrices. Determinants; minors and cofactors;evaluation by row and column manipulation. Application of matrix methods to the solution of simultaneouslinear equations; cases in which solutions are unique, non-unique, or, do not exist.

Ordinary differential equations: Classification and terminology. Linear homogeneous differential equa-tions and superposition. First order linear differential equations, integrating factors. Second order lineardifferential equations with constant coefficients.; complementary functions and particular integrals; applica-tions to damped and forced vibrations. Simultaneous linear differential equations; solutions by eliminationand by a suitable choice of coordinates.

References

1. Mathematical Methods in the Physical Sciences, 2nd Edition, M.L.Boas, John Wiley, New York, 19832. All you wanted to know about Mathematics but were afraid to ask: Mathematics for Science Students,

L.Lyons, Cambridge University Press, Cambridge, 19983. The mathematics of Physics and Chemistry, H.Margenau and G.M.Murphy, Van Nostrand, Princeton,

19624. Higher Algebra, A.Kurosh, Mir Publishers, Moscow, 19725. Mathematical Methods for Physicists, 4th. Edn., G.B.Arfken and H.J.Weber, Academic Press, New

York, 1995, (Prism Books, Bangalore, India)6. Matrices, F.Iyres. Jr.,, (Schaum series), Tata McGraw-Hill, New Delhi, 1973

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3.3. Mathematics4

Multiple integrals: Double integrals and their evaluation by repeated integration in Cartesian, plane polarand other specified coordinate systems. Jacobians. Line, surface and volume integrals, evaluation by changeof variables (Cartesian, plane polar, spherical polar coordinates and cylindrical coordinates only.). Integralsaround closed curves and exact differentials. Greens theorem in the plane.

Vector analysis: Scalar and vector fields. The operations of grad, div and curl and understanding anduse of identities involving these. The statements of the theorems of Gauss, Green and Stokes with simpleapplications. Conservative fields.

Complex variables: Functions of a complex variable. Differentiation. The Cauchy-Riemann conditions.Analytic functions. Harmonic nature of the real and imaginary parts of an analytic function. Cauchysintegral theorem and its proof using Stokess theorem. Multiply connected regions. Cauchys integralformula. Calculation of the n-th derivative of an analytic function using Cauchys integral formula. TheTaylor expansion. The Laurent expansion. Types of isolated singularities; removable, poles and essentialsingularities and branch points. The residue theorem. Evaluation of simple integrals using residue theorem.The Cauchy principal value.

References

1. Mathematical Methods in the Physical Sciences, 2nd Edition, M.L.Boas, John Wiley, New York, 19832. Mathematical Methods for Physicists, 4th. Edn., G.B.Arfken and H.J.Weber, Academic Press, New

York, 1995, (Prism Books, Bangalore, India)3. The theory of functions of a complex variable, A.G.Sveshnikov and A.N.Tichonov, Mir Publishers,

Moscow, 1971

3.4. Waves and Optics

Huygen principle: The Huygen principle and its application to the derivation of the laws of reflection andrefraction (at a plane surface) and the (thin) convex lens formula.

Interference: Simple two slit interference (restricted to slits of negligible width). The diffraction grating,its experimental arrangement and conditions for proper illumination. The dispersion and resolution ofa diffraction grating. A brief mention of the methods of producing diffraction gratings. The standardMichelson interferometer as an example of two beam interference by division of amplitude. Localisation offringes produced by an extended source. The Michelson-Morley experiment.

Diffraction: Fraunhofer diffraction by a single slit including experimental arrangements; application toresolution of a single lens. The zone plate.

Polarisation: The slit-string mechanical model for demonstrating polarisation of a wave. Demonstration ofpolarisation of light using two polaroids. A brief mention of the production of polarised light by the followingmethods; reflection at a plane surface - Brewsters law, refraction, i.e., passage through a pile of glass platesand selective absorption of light by a dichroic filter. The polaroid.

The phenomenon of double refraction in a slab of Iceland sparordinary and extra-ordinary rays. Opticaxis. Definition of a uni-axial crystal. Positive and negative uni-axial crystals; principal refractive indices.Definition of birefringence. Quarter- and half-wave plates. The definition of a compensator. Production andanalysis of linearly, circularly and elliptically polarised light. A qualitative description of partially polarisedlight and unpolarised light. Optical activity. Fresnels theory of optical activity.

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The Kerr effect. The photo-elastic effect. The magneto-optic effect; Verdets constant.

References

1. Optical Physics, Third Edition, S.G.Lipson, H.Lipson and D.S.Tannhauser, Cambridge UniversityPress, Cambridge, 1995, Chapters 2, 6, 7, 8, and 9.

2. Principles of Optics, B.K.Mathur, Gopal Printing Press, Kanpur, 1966, Chapters 8 to 16.3. Contemporary Optics, A.K.Ghatak and K.Thyagarajan, Macmillan of India, New Delhi, 19844. University Physics, 4th. Edn., F.W.Sears and M.W.Zemansky, Addison-Wesley, Reading, Massachusetts,

1973, Chapters 36 to 42

3.5. Lab-3: Electronics Laboratory1

Any eight of the following:

1. Study of the charging and discharging of a capacitor2. Verification of Thevenins and maximum power transfer theorems3. Study of passive filters LR, LC and RC4. Study of the junction diode and the zener diode5. Junction transistor characteristics6. Transistor CE amplifier - frequency response and gain7. Emitter followertransistor version8. Construction of a regulated power supply using 78xx and 79xx 3-pin regulators9. OPAMP - parameters, frequency response, gain in the two modes10. Emitter followerusing IC 74111. Voltage dividerusing IC 741

Semester-IV

4.1. Electronics2

Field Effect Transistors: Introduction. FET characteristics. FET types; MOSFET, JFET. Basic FETcircuits; JFET current sources. FET amplifiers. Source followers. FET gate current. FETs as variableresistors. FET analog switches. (Pages 113-145).

Feedback and operational amplifiers: Introduction to the concept of feedback. Operational amplifiers.The golden rules. Basic op-amp circuits; Inverting amplifier. Non-inverting amplifier. Follower. Currentsources. Basic cautions for op-amp circuits. A brief mention of the departure from ideal op-amp behaviour.(Pages 175-213)

Active Filters and oscillators: Frequency response with RC filters. Ideal performance with LC filters.over-view of active filters. Key filter performance criteria. Filter types; Butterworth and Chebyshev. Besselfilter. Active filter circuits; VCVS circuits. Oscillators; introduction. Relaxation oscillators; the classic timerchip 555. Voltage controlled oscillators. Wien bridge and LC oscillators. Quartz crystal oscillators. (Pages284-303)

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Voltage regulators and Power circuits: Introduction. The unregulated power supply; three wire connection,line filter and transient suppressor, fuse, shock hazard, transformer, filter capacitor, rectifier. A brief intro-duction to the following: the 723 regulator, three and four terminal regulators, pass transistors, switchingregulators and dc-dc converters. (Pages 307-368)

Basic logic concepts: Logic states. Voltage range of high and low. Number codes; Hexadecimal repre-sentation; BCD; Signed numbers; Arithmetic in 2s complement; Gray code. Gates and truth table; ORgate; AND gate; Inverter (the NOT function); NAND and NOR; Exclusive-OR. A brief mention of the TTLand CMOS family of logic ICs. Combinational logic; Logic identities; example of making an exclusive ORfunction from ordinary gates. A brief mention of the combinational functions available as ICs. Sequentiallogic; devices with memory: flip-flops.(Pages 471-512)

References

1. The page numbers mentioned above refer to the following book: The art of electronics: P. Horowitzand W. Hill, Second Edition, Cambridge University Press, 1995.

4.2. Electromagnetism1

Electrostatics in vacuum: Coulombs law. Electric field due to a system of charges. Field lines, flux andGausss law. Gausss law in differential form. The electric dipole; its electric field and potential. The coupleand force on, and the energy of, a dipole in an external electric field. Gausss law in integral form; fieldand potential due to surface and volume distributions of charge. Force on a conductor. The capacitanceof parallel plate. Cylindrical and spherical capacitors. Electrostatics in the presence of dielectric media.Modification to Gausss Law. polarisation, the electric displacement, relative permittivity. Capacitance andenergy in the presence of dielectric media.

Magnetic effects in the absence of magnetic media: The B-field. Steady currents: The B-field set up bya current; the Biot-Savart Law. The force on a current and on moving charges in a B-field. The magneticdipole; its B-field. The force and couple on, and the energy of, a dipole in an external B-field. Energy storedin a B-field. Gausss Law in integral form. Simple cases of the motion of charged particles in electric andmagnetic fields.

References

1. Introduction to Electrodynamics, Third Edition: David J. Griffith, Prentice-Hall of India, New Delhi,1999

2. Electricity and Magnetism, Berkely Physics Cource, Vol. 2, E.M.Purcell, McGraw-Hill, 1965, NewYork

3. Electricity and Magnetism, A.N.Matveev, Mir Publishers, Moscow, 1986

4.3. Elasticity and Hydrodynamics

Hookes law: Hookes law. Elastic potential energy. Elastic moduli for isotropic materials. Relationsbetween elastic constants.

Bending of bars: Bending moment; uniform and non-uniform bending. Theory of the light cantilever.I-section girder; Torsion of a circular cylinder, couple per unit twist. Torsion pendulum.

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Surface tension: Forces on a liquid surface; surface energy; effect of impurities. Pressure within a curvedsurface -examples. Experimental determination of surface tension; the drop weight method and the Quinckesmethod.

Fluid statics: Equilibrium equation. Pressure at a given depth in a fluid. Laws of flotation. Equilibriumof a floating body. Stability of equilibrium; Metacentre and determination of metacentric height.

Hydrodynamics: Hydrodynamics of an ideal, non-viscous fluid; equation of continuity. Eulers equationsof motion. Bernoullis theorem; simple applications.

References

1. Fundamentals of Physics, Extended 3rd. Edn., D.Halliday, R.Resnick and J.Merryl, John Wiley, NewYork, 1988

2. University Physics, 4th. Edn., F.W.Sears and M.W.Zemansky, Addison-Wesley, Reading, Massachusetts,1973, Chapters 12, 13 and 14

4.4. Mathematics5

Relations and functions: Relations. Cartesian product of sets. Binary relation on a set. Equivalenceclasses. Partition of a set. Mappings; injective, surjective and bijective. Composite map. Inverse map.Binary operations. The composition table for a binary operation.

Algebraic systems: Examples of integers, rationals, the residue classes of integers and two by two matrices.

Groups: Group axioms. Order of a (finite) group. Examples of the set of natural numbers, the set ofintegers, the set of rationals and the set of reals as groups under number addition. Example of the groupof all m n real matrices under matrix addition. The example of the group of all real 2 2 real matricesunder matrix multiplication. Definition of an Abelian group. The uniqueness of the identity and inverse in agroup. The properties (a1)1 = a and (ab)1 = b1a1. The left and right cancellation laws. Solving theequation ax = b for x in a group. The example of the Klien 4-group. Integral powers and the law of indicesin a group. Subgroups; definitions of proper and improper subgroups, the proposition that the intersectionof any two subgroups of group is a subgroup, the conjugate subgroup tHt1 of the subgroup H in a groupG, normal subgroup, centre of a group. Cosets. Lagranges theorem that (in a finite group) the order ofevery subgroup is a divisor of the order of the group. Cyclic groups. Examples. The proposition that everycyclic group is abelian and every subgroup of a cyclic group is cyclic (and not conversely). The order of anelement in a group. The proposition that every group of prime order is cyclic and hence is abelian. Theproposition that, in a finite group, every element is of a finite order and the order of the element divides theorder of the group. The class generated by an element of a group and its properties. The division of a groupinto mutually disjoint classes.

Homomorphism and isomorphism of groups: Definitions of homomorphic and isomorphic mappings.The properties (e) = e, (a1) = ((a))1 of an isomorphism : G 7 G. The propositions that thecomposition and inverse of a isomorphism are themselves isomorphic.

The Symmetric Group Sn: Definition of a permutation and the composition of permutations. Groupstructure of Sn. The proposition that Sn is non-abelian for n 3. Cycles of length r. Transpositions.Disjoint cycles. The proposition that every element of Sn can be expressed as a product of disjoint cyclesand the corollary that every permutation is a product of transpositions. The signature of a permutation.The classes of the groups S3 and S4.

Rings, Integral Domains and Fields: Definitions of a ring. Example of the ring of 2 2 matrices. The

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proof of the relations a.0 = 0.a = 0, and a(b) = (a)b = ab. Rings with unity; definition; the uniquenessof the identity; invertible elements and the uniqueness of inverse. Integral domain; definition; proof of theproposition that ab = ac implies a = 0 or b = c; proof of the proposition that in a finite integral domain,every non-zero element is invertible. Fields; Definition; examples of the fields of rationals, reals and complexnumbers. Proof of the proposition that every field is an integral domain (and not conversely).

Vector Spaces: Definition. Examples of Rn, Cn, the set of all mn real matrices, the solutions of a secondorder linear ODE, and the set of all continuous functions from (0, 1) to R. Definition of a subpace. Lineardependence and independence.

References

1. Text book of algebra produced by the Leadership Project Committee (Mathematics), University ofBombay, Tata McGraw-Hill, New Delhi, 1987, Chapters 2, 4, 5 and 6.

2. Linear algebra and group theory for physicists, K.N.Srinivasa Rao, New Age International, New Delhi,1996, Chapters 1, 2 and 3.

3. Higher Algebra, A.Kurosh, Mir Publishers, Moscow, 1972

4.5. Lab-4: Properties of Matter

Any eight of the following:

1. g by bar pendulum2. g by light spiral spring3. g by Katers pendulum4. Youngs modulus by single cantilever5. Youngs modulus by stretching6. Torsion pendulumdetermination moment of inertia and rigidity modulus7. Searles double bar- determination of elastic moduli and Poissons ratio8. Coefficient of viscosity by capillary flow method9. Inversion temperature of copper-iron thermocouple10. Law of intermediate metals11. Thermal conductivity by Forbess method12. Modes of vibration of a fixed-free strip

Semester-V

5.1. Chemistry1

Stoichiometry: The origins of atomic theory, determination of atomic weights and molecular formulas, themole concept. The chemical equation. Stoichiometric calculationsexamples and problems.

Oxidation-reduction reactions: Oxidation states. The half-reaction concept. Balancing oxidation-reductionreactions.

12

Chemical equilibrium: The nature of the chemical equilibrium; equilibrium constant and calculations withequilibrium constants.

Thermochemistry: Enthalpy, standard enthalpy change, illustration of Hesss law of constant heat ofsummation, enthalpy of formation of compounds. Review of entropy and second law of thermodynamics.Free energy and equilibrium constants, temperature dependence of equilibria, colligative properties.

Chemical kinetics: Law of mass action, reaction rate, rate constant, elementary processesmolecularityand the order a reaction. Rate laws, examples of simple reactions, determination of the rate constants andthe order order of a reaction. Effect of temperature on reactionsArrhenius equation. (24 Hours)

Periodic properties of elements: The periodic table, electrical and structural properties, ionization energy,electron affinity, electronegativity, oxidation states, size relationships, chemical properties of the oxides, theproperties of the hydrides.

The Elements of the Groups I-IV: General properties of the alkali metals. The elements of Group III A:boron; aluminium. The elements of Group IV A: carbon; silicon; germanium; tin and lead.

The non-metallic elements: The elements of Group V A; nitrogen, nitrides, oxides of nitrogen, oxyacidsof nitrogen, nitrogen halides and oxyhalides; phosphorous, phosphorous halides and oxyhalides; arsenic;antimony; bismuth. The elements of Group VI A; oxygen; sulphur; selinium and tellurium. The elements ofGroup VII A; halogens, the hydrogen halides, the interhalogen compounds; the noble gas compounds.

Transition elements: A brief discussion of the general properties of the transitional metals. Innertransitionelementstheir position in the periodic table, magnetic and spectral properties and separation. (24 Hours)

References

1. University Chemistry, 3rd. Edn., B.H.Mahan, Narosa (Addison-Wesley), New Delhi, 1975, Chapters1, 5, 7, 8, 9, 13, 14, 15 and 16.

2. Physical Chemistry, 3rd. Edn., F.Daniels and R.A.Alberty, Wiley, New York, 19663. Physical Chemistry, 3rd. Edn., G.M.Barrow, McGraw-Hill, New York, 19734. Advanced Inorganic Chemistry, 3rd. Edn., F.A.Cotton and G.Wilkinson, Interscience, New York, 19725. Theoretical Inorganic Chemistry, M.C.Day and J.Selbin, Reinhold, New York, 1962

5.2. Electromagnetism2

Magnetic media: Magnetisation, the H-field, magnetic permeability. Amperes Law in integral form.Simple cases of the motion of charged particles in electric and magnetic fields. Energy in the presence ofmagnetic media. The electromagnet.

Electromagnetic induction: The laws of Faraday and Lenz. Self and mutual inductance; calculation forsimple circuits. The transformer. Alternating currents; R.M.S. Values; Circuits: Growth and decay ofcurrents in LCR circuits. the use of complex impedance in circuit analysis under steady state conditions;response of an LCR circuit to sinusoidal voltages; Series and Parallel resonance; Half-power frequency, band-width and quality factor Q; power in electrical circuits, the maximum power transfer theorem. Measurementof voltage, current, power and frequency using a CRO.

References

1. Introduction to Electrodynamics, Third Edition: David J. Griffith, Prentice-Hall of India, New Delhi,1999

13

2. Electricity and Magnetism, Berkely Physics Cource, Vol. 2, E.M.Purcell, McGraw-Hill, 1965, NewYork

3. Electricity and Magnetism, A.N.Matveev, Mir Publishers, Moscow, 1986

5.3. Kinetic Theory and Statistical Mechanics

Maxwells distribution of velocities: Derivation of Maxwells velocity distribution using the Boltzmannfactor; experimental verification. Density of states. Equipartition of energy. Simple applications to idealparamagnet, simple harmonic oscillator and perfect gas.

Kinetic theory: Calculation of averages using Maxwells distribution of velocities; derivation of pressure,mean free path, thermal conductivity and viscosity; dependence on pressure and temperature.

Elements of Quantum statistics: Bosons and Fermions. Indistinguishability of identical particles. Aheuristic criterion for indistinguishability. The Bose and Fermi distributions (derivations not required). TheMaxwell distribution as a limiting case of the Bose and Fermi distributions. Fermi energy. The chemicalpotential and its significance.

References

1. Statistical Mechanics, K.Huang, Wiley Eastern, New Delhi, 19752. Fundamentals of Physics, Extended 3rd. Edn., D.Halliday, R.Resnick and J.Merryl, John Wiley, New

York, 19883. Molecular Physics, A.N.Matveev, Mir Publishers, Moscow, 1985

5.4. Quantum Physics

Limitations of classical physics: Qualitative discussions of the problem of the stability of the nuclearatom. The photo-electric effect. Franck-Hertz experiment and the existence of energy levels. Experimentalevidence for wave-particle duality; X-ray diffraction and Bragg law. Compton scattering. Electron andneutron diffraction. Einstein and de Broglies relations (E = h, p = h/).

Schroedinger equation: The concept of the wave function as a probability amplitude and its probabilisticinterpretation. Plane wave solutions of the one-dimensional time-dependent Schroedinger equation for aparticle in free space and elementary derivation of the phase and group velocities (quantitative discussion ofwave packets is not required).

Uncertainty relation: The position-momentum uncertainty relation and simple consequences. Qualita-tive wave mechanical understanding of the size and stability of the hydrogen atom. Solutions of the one-dimensional Schroedingers equation for an infinite square well potential; qualitative treatment of the finitewell (derivation not required). Reflection and transmission at potential steps. Qualitative treatment of bar-rier penetration for simple rectangular barriers. Simple examples and comparison with classical mechanics.

References

1. L.I.Schiff, Quantum mechanics 3rd. Edn. McGraw-Hill Kogakusha Ltd. New Delhi 1968.2. E.Merzbacher, Quantum mechanics, John Wiley, New York3. Richtmyer, Kennard and Lauritsen, Introduction to Modern Physics

14

4. Wehr, Richards and Wehr, Physics of the atom5. Fundamentals of Physics, Extended 3rd. Edn., D.Halliday, R.Resnick and J.Merryl, John Wiley, New

York, 1988

5.5. Lab-5: Optics

Any eight of the following:

1. Newtons ringsdetermination of wavelength2. Determination of Cauchys constants A and B3. Interference at a wedge4. Diffraction grating: wavelength of Mercury lines5. Biprism6. Lloyds mirror7. Diffraction at a straight edge8. Diffraction due to a thin wire9. Diffraction haloes10. Laser experiments

Semester-VI

6.1. Chemistry2

Organic chemistry: The chemistry of hydrocarbons: alkanes, alkenes, alkynes, alkadienes, alicyclic hy-drocarbons, benzene, naphtalene. Common functional groups. Chemistry of alchohols, amines, carbonylcompounds, amides, carbolic acid, esters and aromatic compounds.

Steriochemistry: Meaning of the term isomerism, isomers, tautomers, chirality, enantiomers, diastomers,optical activitydextro and laevo rotations, racemization, geometrical isomerism, R, S, D and L concepts.

Industrial organic chemistry: Basic concepts on coal and oil, dyes, detergents and synthetic polymers.(32 Hours)

Biochemistry: Basic chemistry of natural products: Lipids, carbohydrates, proteins, nucleic acids and theirbiological functions.

References

1. University Chemistry, 3rd. Edn., B.H.Mahan, Narosa (Addison-Wesley), New Delhi, 1975, Chapters17 and 18

2. Advanced Inorganic Chemistry, 3rd. Edn., F.A.Cotton and G.Wilkinson, Interscience, New York, 19723. Theoretical Inorganic Chemistry, M.C.Day and J.Selbin, Reinhold, New York, 19624. Advanced General Organic Chemistry, S.K.Ghosh, Books and Allied (P) Ltd., Calcutta, 1988.5. Organic Chemistry, 3rd. Edn. R.T.Morrison and R.N.Boyd, Allyn and Bacon, Boston, 19736. Modern Topics in Biochemistry, T.P.Bennett and E.Frieden, Macmillan, New York, 19667. A Brief Introduction to Biochemistry, R.J.Light, Benjamin, New York, 1968

15

6.2. Classical Electrodynamics

Preliminaries: Electrodynamics before Maxwell; the laws of Gauss, Faraday, Ampere and the equation B = 0. Maxwells correction of Amperes law; the displacement current. Maxwells equations in freespace. The equation of continuity. Energy density and energy flux density. Poyntings theorem.

Electromagnetic waves in vacuum: The wave equation for E and B. Monochromatic plane wave solutions.Energy and momentum of electromagnetic waves; radiation pressure.

Dielectric media: Polarisation density and electric displacement vector. Dielectric permittivity and sus-ceptibility. Boundary conditions on E and D at the interface between two dielectrics.

Magnetic media: Magnetisation density and magnetic field strength H; Magnetic permeability and sus-ceptibility; Boundary conditions on B and H at the interface between two magnetic media.

Maxwells equations in dielectric and magnetic media: Electromagnetic waves in dielectrics. Refractiveindex and impedance of the medium.

The Lorentz force: Force on a charged particle in an external electromagnetic field. Determination of thee/m of the electron; the methods of Thomson and Dunnington. Determination of the charge of the electronby the Millikan oil-drop method.

References

1. Introduction to Electrodynamics, Third Edition: David J. Griffith, Prentice-Hall of India, New Delhi,1999

2. Electricity and Magnetism, Berkely Physics Cource, Vol. 2, E.M.Purcell, McGraw-Hill, 1965, NewYork

3. Electricity and Magnetism, A.N.Matveev, Mir Publishers, Moscow, 1986

6.3. Atomic, Molecular and Solid State Physics

Atomic Physics: The Bohr model of the hydrogen-like atom. A brief account of the Sommerfeld model(detailed derivations not expected). Electron spin; Stern-Gerlach experiment. Space quantisation. Thevector model of the atom. Spin-orbit interaction. Fine structure of spectral lines. The Pauli exclusionprinciple and the electronic configuration of atoms; LS and JJ coupling. The normal Zeeman effect. Paschen-Back effect. Stark effect.

Light scattering by molecules: Tyndall, and Rayleigh scattering. Fluorescence and phosphorescence.Raman effect. Elementary theory. Experimental techniques. Intensity and polarisation of Raman lines.Applications of Raman effect.

X-ray diffraction: Braggs law. The Bragg spectrometer. Types of crystals. Miller indices. The structureof NaCl and KCl crystals. Continuous and characteristic X-ray spectra. Mosleys law.

Free electron theory of metals: Electrical conductivityclassical theory. Sommerfelds model. Free electrongas. Density of energy states. Fermi energy. Average energy of electrons. Variation of Fermi energy andaverage energy with temperature. Electronic specific heat. Paramagnetism of free electrons. Thermionicemission from metals. Electrical conductivity. Drift velocity and relaxation time. Thermal conductivity.Wiedemann-Franz law.

Band theory of solids: Elementary ideas regarding formation of energy bands. Bloch equations. One-dimensional Kronig-Penney model. Density of states. Effective mass. Energy gap. Distinction betweenmetals, insulators and intrinsic semiconductors. Concept of holes.

16

Superfluidity and Superconductivity: Superfluidity: The two-fluid model; properties of liquid helium.Superconductivity: Experimental facts, Meissner effect, critical magnetic field, type-I and type-II super-conductors. Phenomenological theory, London equations. High frequency behaviour. Thermodynamics ofsuperconductors. Specific heat in the superconducting state. Qualitative ideas relating to the theories ofsuperconductivity.

References

1. Solid State Physics, A.J.Dekker, Macmillan, London.2. Fundamental University Physics, M.Alonso and E.J.Finn, Addison-Wesley, Reading, Massachusetts,

19673. University Chemistry, B.H.Mahan, Narosa, New Delhi, 1986, Chapters 3 and 104. Introduction to Solid State Physics, 7th Edn., C.Kittel, John Wiley, New York.5. Solid State Electronic Devices, 2nd Edn., B.G. Streetman, Prentice-Hall of India, New Delhi, 1983.6. Fundamentals of Solid State Physics, B.S.Saxena , R.C.Gupta and P.N.Saxena Pragathi prakashana,

Meerut.

6.4. Nuclear and Particle Physics

Radioactivity: Successive disintegration, Radioactive equilibrium, Radioactive series, Unit of radioactivity.Range and energy of particles-their measurements. Theory of alpha decay (qualitative), Geiger-Nuttal Law.Beta ray spectra, Pauli neutrino hypothesis. K- electron capture. Internal conversion, Gamma ray spectrum,Nuclear isomerism, Radioactive carbon dating and age of the earth.

Accelerators and mass spectrometers: Linac, Cyclotron, betatron and principle of electron synchrotron.Dempsters mass spectrograph,

Nuclear detectors: Gas filled detectors, Scintillation detectors, and Semiconductor detectors (qualitativetreatment only).

Nuclear Structure: Rutherfords nuclear-atom model, properties of the nucleus-mass, size and density,charge, spin and magnetic moment (qualitative).

Nuclear Models: Liquid drop model, semi-empirical mass formula. Shell model and magic numbers (qualitative).

Nuclear Reactions: Q-values, Threshold energy, Reactions induced by proton, Deutron and particles,Photodisintegration.

Nuclear Fission: Explanation, Estimation of fission energy on the basis of liquid drop model, controlledand uncontrolled chain reactions. Four factor formula. Types of reactors-Swimming pool and fast breeder.Radiation protection and Radiation units.

Nuclear Fusion: Thermo-nuclear reactions. Sources of stellar energy. C-N cycle and the proton-protoncycle. Electric and magnetic confinement of plasma. Tokomak.

Cosmic Rays: Primary and secondary cosmic rays, showers, geomagnetic effects. Composition and originof cosmic rays.

Fundamental particles: Particles and antiparticles. Classification of particles. Mention of the basicinteractions in nature.

17

References

1. Fundamental University Physics, M.Alonso and E.J.Finn, Addison-Wesley, Reading, Massachusetts,1967

2. University Chemistry, 3rd. Edn., B.H.Mahan, Narosa, New Delhi, 1986, Chapter 193. Principles of Modern Physics, Leighton, McGraw-Hill, New York4. Nuclear Physics, Kaplan5. The atomic nucleus, R.D.Evans, Tata McGraw Hill, New Delhi6. Cosmic rays, Bruno Rossi7. Cosmic rays, Janossy8. Nuclear Physics, R.C.Sharma, K.Nath and Company, Meerut9. Concepts of nuclear Physics, B.L.Cohen, Tata McGraw-Hill, New Delhi10. Nuclear Physicsan introduction, S.B.Patel, Wiley-Eastern, New Delhi

6.5. Lab-6: Electricity and Modern Physics

Any eight of the following:

1. B H curve and hysteresis loss2. Self-inductance by Andersons bridge3. High resistance by leakage4. Helmholtz galvanometer5. Verification of Stefan-Boltzmann law6. e/m of electron by Thomsons method7. Rydbergs constant8. Half-life of K-409. h using photocell10. Inverse square law of gamma rays11. Inter-planar distance using an X-ray photograph12. Frank-Hertz experiment

Semester-VII

7.1. Mathematical Methods of Physics1

Partial differential equations: Separation of the Helmholtz equation in Cartesian coordinates, circularcylindrical coordinates and spherical polar coordinates and identification of the ordinary differential equations(ODEs) involved.

The Gamma function: The Gamma function (x) defined as a definite integral (Euler). Evaluation ofthe error integral (1/2). The factorial notation. Proof of the basic property (x + 1) = x(x). TheStirling formula (Derivation not required.) The Beta function as an integral and its relation with the gammafunction.

18

Second order ODEs: Ordinary and singular points of a general second order ODE. The Frobenius methodof series solution. (Proofs of the theorems not expected.) Example of the Bessel Equation; series solutionabout x= 0. Linear dependence and independence of solutions; the wronskian.

Bessel functions: Generating function. Recurrence relations. Definition of Neumann functions and theirbehaviour near x=0. Definition of Hankel functions and spherical Bessel functions:

Legendre polynomials: Generating function. The recurrence relation The Legendre differential equation(solution not required). Parity. Orthogonality. Legendre series. Rodrigues formula. Associated Legendrepolynomials. Orthogonality. Definition of Spherical Harmonics. Orthogonality of spherical harmonics (proofnot required).

Hermite functions: Generating functions for Hermite polynomials. The Recurrence relations. Parity.Rodrigues representation. Orthogonality.

Laguerre functions: Differential equation. Generating function. Recurrence relations. Rodrigues formulafor associated Laguerre polynomials. (proof not required)

Fourier series and transforms: Examples; saw-tooth wave, square wave and the Riemann Zeta function.Change of interval. Exponential form of the Fourier integral. Example of the Finite wave train.

Integral equations: Fredholm and Volterra types. Method of the Neumann series for equations of thesecond kind. Equations with separable kernels and their reduction to a system of simultaneous algebraicequations. Transformation of a linear second order differential equation into an integral equation. Exampleof the linear oscillator. Hilbert Schmidt theory of equations with symmetric kernels. Non-homogeneousintegral equations.

References

1. Mathematical Methods for Physicists, 4th. Edn., G.B.Arfken and H.J.Weber, Academic Press, NewYork (Prism Books, Bangalore, India), 1995

2. The mathematics of Physics and Chemistry, H.Margenau and G.M.Murphy, Van Nostrand, Princeton,1962

3. Mathematical Physics, P.K.Chattopadhay, Wiley Eastern, New Delhi, 1990

7.2. Mathematical Methods of Physics2

Linear operators: Linear operators over an n-dimensional linear vector space Vn. Matrix representative ofa linear operator in a given basis of Vn. The algebra of linear operators. Effect of change of basis. Activeand passive points of view. Invariant subspace and the eigenvalue problem of a linear operator. ComplexEuclidean space; scalar product, norm, Schwarz inequality, orthogonality. The Schmidt orthogonalisationprocedure. Scalar product in terms of the components of a vector. The adjoint of a linear operator. Normaloperator. The Schur canonical form. Direct product of two vector spaces the Kronecker product space.

Linear representations of groups: Groups of regular matrices; the general linear groups GL(n, C) andGL(n, R). The special linear groups SL(n, C) and SL(n, R). The unitary groups U(n). and SU(n). Theorthogonal groups O(n, C), O(n, R), SO(n, C) and SO(n, R) . The symplectic group Sp(2n, C). (Only thegroup structure of these groups need be discussed.)

The matrix exponential function: Definition and properties. The definition of the linear representation ofgroup. Schur lemma. The representation of the direct product of two groups. Elements of the representationtheory of matrix groups. The rotation matrix. Euler resolution of the rotation matrix. A brief introductionto the irreps of the rotation group SO(3, R).

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Tensors: Tensor as an element of a linear vector space. Law of transformation of tensor components undera change of coordinates. Addition, scalar multiplication, outer multiplication and contraction of tensors.The Levi-Civita pseudo tensor. Volume tensors. Riemannian metric and covariant differentiation of tensorfields. Gradient, divergence, curl and Laplacian in arbitrary curvilinear coordinates.

References

1. Linear algebra and group theory for physicists, K.N.Srinivasa Rao, New Age International, New Delhi,1996, Chapters 1, 2 and 3.

2. Classical Groups for Physicists, B.G.Wybourne, John-Wiley, New York, 19743. Higher Algebra, A.Kurosh, Mir Publishers, Moscow, 19724. Mathematical Methods for Physicists, 4th. Edn., G.B.Arfken and H.J.Weber, Academic Press, New

York (Prism Books, Bangalore, India), 1995

7.3. Mechanics3

Motion in a non-inertial frame:Motion of a point particle in a general (rigid) non-inertial frame of reference.Galilean relativity. Larmor theorem.

Mechanics of a system of particles: Center of mass. Conservation of linear and angular momentum inthe absence of (net) external forces and torques. The energy equation and the total potential energy of asystem of particles.

Constrained motionthe Lagrangean method: Types of constraints. Generalised coordinates. DAlembertsprinciple and Lagrangean equations of the second kind. Velocity dependent potential; the Lagrangean for acharged particle in an external electromagnetic field. Examples of Lagrangean for (i) single particle in threedimensions in Cartesian, spherical polar and cylindrical polar coordinates, (ii) the Atwood machine and (iii)a bead sliding on a rotating wire in a force-free space.

Mechanics of rigid bodies: Angular momentum and kinetic energy of motion about a point. Moments andproducts of inertia; the inertia tensor. Eulers equations of motion. Torque free motion of a rigid body.

Small oscillations: Normal modes. The vibrational modes of the CO2 molecule.

Hamiltons principle: Derivation of Lagranges equation from Hamiltons principle.

Hamilton equations: Cyclic coordinates. Derivation of Hamiltons equations from a variational principle.Canonical transformations; examples. Poisson brackets; equation of motion in the Poisson bracket notation.The Hamilton-Jacobi equation; the example of the harmonic oscillator.

Continuum Mechanics: Small deformations of an elastic solid; the strain tensor. Meaning of the straintensor components-tensile, shearing and volume strains. The stress tensor. The relation between the stresstensor and the stress vector at a point of a strained elastic medium. Equations of equilibrium and thesymmetry of the stress tensor. Meaning of the stress tensor components-the normal and shearing stresses.

Hookes law: The generalised Hooke law for a homogeneous elastic medium; the elastic modulus tensor. Abrief discussion of the number of independent components of the elastic modulus tensor and its reductionunder symmetries of the medium. The Lame constants for a homogeneous isotropic elastic medium. Thestrain energy function.

Naviers equations: Naviers equations of motion for a homogeneous isotropic medium; force-free motionof an unbounded isotropic homogeneous medium; irrotational and solenoidal waves.

20

Fluid mechanics: Equation of continuity. Eulers equation of motion of an ideal fluid. The steady incom-pressible flow of an ideal fluid - Bernoullis theorem. Simple applications.

Flow of a viscous fluid: Navier-Stokes equation and its solution for the case of a flow through a cylindricalpipethe Poiseulle formula.

References

1. Classical Mechanics, H.Goldstein2. Classical Mechanics, L.D.Landau and E.M.Lifsitz3. Theory of Elasticity, L.D.Landau and E.M.Lifsitz4. Fluid Mechanics, L.D.Landau and E.M.Lifsitz5. Mechanics K.R.Simon6. Tensor Analysis, I.S.Sokolnikoff

7.4. Classical Electrodynamics2

Potential formulation: Scalar and vector potentials. Gauge transformation. The coulomb and Lorentzgauges. Retarded potentials. Lienard-Wiechert potentials and the electric and magnetic fields of a movingpoint charge. The special case of a charge moving with a constant velocity.

Multipole moments: The electric dipole and multipole moments of a system of charges. The magneticmoments of a system of charges in stationary motion.

Electromagnetic waves: The radiation gauge for source-free electromagnetic fields. The wave equation forA. Monochromatic plane waves. Wavelength, frequency, velocity, phase and polarisation of a monochromaticplane wave. The 4-dimensional wave vector and Doppler effect.

Partially polarised light: The hermitian polarisation tensor . Characterisation of totally polarised,partially polarised and natural light in terms of . Degree of polarisation. Stokes parameters.

Radiation: Signature of radiation. Electric and magnetic dipole radiation. Radiation from an arbitrarysource. Power radiated by a point charge. Larmor formula. Lienards generalisation of the Larmor formula.Radiation reaction; Abraham-Lorentz formula.

References

1. The Classical Theory of Fields, 4th. Edn., Pergamon Press, 1985, Sections 18, 23, 24, 25, 40 and 41.2. Introduction to Electrodynamics, 3rd. Edn., D.J.Griffiths, Prentice-Hall of India, New Delhi, 1999,

Chapters 10 and 11.3. Principles of Optics, M.Born and E.Wolf, 6th. Edn., Pergamon Press, Oxford, 1980

7.5. Lab-7: Electronics Laboratory2

Any eight of the following:

1. Study of basic gates- AND, OR, NOT, NAND, NOR, EX-OR gates2. FET characteristics

21

3. Universality of NAND, NOR gates4. Circuits for Boolean expressions5. Half-adder and Full-adder6. Encoders and decoders7. Timer circuits using IC 7418. IC oscillators using IC 7419. Flip-flops using IC 741- Astable, Bistable10. RS and JK Flip-flops11. Shift registers12. Microprocessors

Semester-VIII

8.1. Quantum Mechanics1

Fundamental concepts: Stern-Gerlach experiment, postulates of quantum mechanics, kets, bras and op-erators, matrix representations, measurements, observables and uncertainty relations. Change of basis, po-sition, momentum and translation. Wave functions in position and momentum space. Quantum dynamics;the Schroedinger and Heisenberg pictures.

Harmonic oscillator: Review of classical oscillatorquantization in coordinate and energy bases. Passagefrom one basis to another.

Symmetries and angular momentum: Translational invariance in quantum theory. Time translationinvariance. Parity invariance. Rotations in two dimensions. Angular momentum in three dimensions.Eigenvalue problem of L2 and Lz.

Hydrogen atom: Solution of the Schroedinger equation. Energy eigenstates, degeneracy. Multi-electronatoms and periodic table.

Multielectron systems: Permutation symmetry. Symmetrization postulate. Two-electron system. Heliumatom.

Approximation methods: Time independent perturbation theory, examples. Degenerate perturbationtheory. Variational and WEB methods.

Path integral formulation of Quantum theory: Case of the free particle and its propagator. Equivalenceto the Schroedinger equation.

References

1. R. Shankar, Principles of Quantum Mechanics 2nd Edn., 1984,Plenum Press, New York

2. J.J.Sakurai, San Fe Tuan (Editor), Modern Quantum Mechanics, Addison-Wesley of India, 19993. L.I.Schiff, Quantum mechanics 3rd. Edn., (McGraw-Hill Kogakusha Ltd. New Delhi 1968)4. V.K.Thankappan, Quantum mechanics 2nd. Edn., Wiley Eastern, New Delhi5. F.Schwabl, Quantum mechanics, Narosa Publishing House, New Delhi6. E.Merzbacher, Quantum mechanics, John Wiley, New York

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8.2. Special Theory of Relativity

Preliminaries: Real coordinates {x0, x1, x2, x3} in Minkowski spacetime; the Minkowski metric ij diag (1 1 1 1).Definition of the general homogeneous Lorentz transformation (HLT) as an element of the real 4 4 ma-trix group O(3, 1). Properties of a HLT and the four disjoint pieces of O(3, 1). The subgroup SO(3, 1) ofproper orthochronous Lorentz transformations. 4-scalars, 4-vectors and 4-tensors and their algebra. Raisingand lowering of indices. Timelike, null, and spacelike vectors and world-lines. The light-cone at an event.Orthogonality of 4-vectors.

Relativistic mechanics of a material particle.: The proper-time interval d along the world-line of amaterial particle. The 4-velocity and 4-acceleration of a material particle. The instantaneous (inertial)rest-frame of a material particle and the components of 4-velocity and 4-acceleration in this frame. Theorthogonality of 4-velocity and 4-acceleration. The rest-mass m0 of a material particle and the definition ofthe relativistic 3-momentum p = mu =

{m0/

1 u2/c2

}(dr/dt). The 4-momentum vector. Statement of

the second law of Newton in the form (dp/d) = f where f is the 3-vector force on the particle. Definition ofthe 4-force Fi and the 4-vector form (dPi/d) = Fi of Newtons law. Determination of the zeroth componentF0 of the 4-force under the assumption dm0/d = 0 along the world-line of the particle. Motion of a particleunder a conservative 3-force field f = and the energy integral E = mc2 + . The rest energy and therelativistic kinetic energy of a particle.

Electrodynamics in covariant form: The 4-potential Ai and the 4-current-density Ji. The Maxwellfield tensor Fij . The dual field tensor Fij . Maxwell field equations in 4-dimensional form. The equation ofcontinuity iJ i = 0. The Lorentz-4-force on a charge. The gauge invariance of Fij in terms of the 4-potential.The two Lorentz invariants of Fij . Lorentz transformation of Fij . Lorentz invariant classification of Maxwellfields into null, non-null, pure electric and pure magnetic fields.

Continuum mechanics: The 4-dimensional action integral for a continuous system. Euler equations ofmotion. The energy-momentum tensor Tij and its Symmetrization. The energy-momentum tensors for theelectromagnetic field, perfect-fluid and incoherent-fluid. (Only the expressions for these tensors are to begiven; a detailed treatment is not expected). The identity jT ij = 0 and its meaning in the cases of theelectromagnetic field and the perfect-fluid.

References

1. The classical theory of fields, 4th Edition, L.D.Landau and E.M.Lifshitz, Pergamon Press, Oxford,1985, Sections 1 to 6, 16 to 18, 23 to 25, 26 to 35.

2. Relativity: The special theory, J.L.Synge, North-Holland, 1972, Chapter 4.

8.3. Optics2

Electromagnetic waves: The electromagnetic wave equation in an isotropic dielectric medium, wave velocityand refractive index, plane wave solutions, flow of energy, review of radiation. Reflection and refraction, theFresnel coefficients (details of working not expected), Brewster angle. Incidence in the denser medium, totalinternal reflection, phase changes on total internal reflection, optical tunnelling, mirages.

Polarisation and anisotropic media: Electromagnetic waves in an anisotropic medium. The dielectrictensor. The index ellipsoid. Characteristic waves. The -surface for a crystal. Ordinary and extraordinaryrays. Conical propagation. Uniaxial crystals and light propagation in them. (Only a summary need begiven; detailed derivations not expected.) Optical activity; phenomenological theory involving a Hermitian

23

dielectric tensor. A brief summary of retardation plates compensators and crystal polarisers. Inducedanisotropy; the electro-optic, photo-elastic and magneto-optic effects.

Multiple beam interference: Generalities; the Fabry-Perot interferometer. Multiple reflections in anamplifying medium. The confocal resonator; transverse modes. Berrys phase in interferometry.

Optical fibres: Geometrical theory of wave guiding. Wave equation for a planar waveguide. Dispersion.Single-mode wave guide. Optical fibres. Step-index fibres. Graded-index fibres. Production of fibres. Abrief introduction to communication through optical fibres.

Coherence: Introduction. Properties of real light waves. The amplitude and phase of quasi-monochromaticlight. The spectrum of a random series of wave groups. White light. The mutual coherence function; theoptical stethoscope and visibility of interference fringes. Temporal coherence; degree of temporal coherence.Spatial coherence; a qualitative investigation, The degree of spatial coherence. The van Cittert-Zernicketheorem; laboratory demonstration of spatial coherence.

References

1. Optical Physics, 3rd Edition, S.G.Lipson, H.Lipson, and D.S.Tannhauser, Cambridge University Press,1995, Chapters 5, 6, 9, 10, 11.

2. Principles of Optics, M.Born and E.Wolf, 6th. Edn., Pergamon Press, Oxford, 1980

8.4. Thermal Physics

Thermodynamics: Preliminaries; first law; second law; entropy; some immediate consequences of thesecond law; thermodynamic potentials; the third law of thermodynamics.

Applications of thermodynamics: Thermodynamic description of phase transitions. Surface effects incondensation. van der Walls equation of state.

Classical statistical mechanics: Liouvilles theorem; the postulate of equal a priori probability ; the micro-canonical ensemble; averages the most probable value and the ensemble average. Equilibrium properties ofa system discussed through the microcanonical ensemble. Derivation of thermodynamics. The generalisedequipartition theorem and the virial theorem; the theorem of equipartition of energy; the relation betweenheat capacity and the number of degrees of freedom and its validity. Classical ideal gas. Gibbs paradox.

Quantum statistical mechanics: The postulates of quantum statistical mechanics. Density matrix. Themicrocanonical ensemble. Third law of thermodynamics. Microcanonical ensemble for ideal Boltzmann,Fermi and Bose gases; the derivation of the corresponding distribution formulae.

Applications of quantum statistics: Equation of state of an ideal Fermi gas (derivation not expected);application to the theory of white dwarf stars; the Chandrasekar limit. Application of the Bose statistics tophotons; derivation of Plancks law; comments on the rest mass of photons. Bose-Einstein condensation.

References

1. Statistical Mechanics, K.Huang, Wiley-Eastern, 1975, Chapters 1, 2, 7, 11 and 12.2. Molecular Physics, A.N.Matveev, Mir Publishers, Moscow, 1985

8.5. Lab-8: Optics Laboratory2

Any eight of the following:

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1. Verification of Fresnels laws of reflection2. Determination of refractive index of a transparent dielectric using Brewsters law3. Determination of birefringence of mica using quarter wave plate4. Determination of birefringence of mica using Babinet compensator5. Fabry-Perot etalon6. Michelson interferometer7. Laser experiments8. Jamins interferometer9. Verification of Brewsters law

Semester-IX

9.1 Atomic and Molecular Physics

Hydrogen and hydrogen-like Systems: Spin of the electron; Pauli-Darwin theory of spin-orbit interaction.Relativistic correction to the energy levels of the hydrogen atom; comparison with Dirac theory. Lamb-shiftand its origin. Alkali Atoms. Helium and atoms with two electrons outside closed shells. Optical pumping,Doppler-free laser spectroscopy. Laser cooling and trapping of atoms and ions.

Molecular spectroscopy: . Overview of molecular spectroscopy. A brief introduction to IR, Raman, NMR,NQR, FTR and microwave spectroscopy.

The chemical bond: Parameters of molecular structure: bond energies, bond lengths and bond angles.Ionic bonds, ionic lattice energies and crystal lattice geometry. The simplest covalent bonds: the hydrogenmolecule ion and the hydrogen molecule. Atomic and molecular orbitals, electron dot structures, and theoctet rule. Molecular geometry; hybridization. Bond polarity. Multiple bonds. Multicenter bonds. Metallicbonding.

Molecular orbitals: Orbitals for homonuclear diatomic molecules. Heteronuclear diatomic molecules.

References

1. Atomic Theory, N.Tralli and P.R.Pomilla, McGraw-Hill, New York2. Fundamentals of Molecular Spectroscopy, C.N.Banwell, Tata McGraw-Hill, New Delhi3. University Chemistry, 3rd. Edn., B.H.Mahan, Narosa (Addison-Wesley), New Delhi, 1975, Chapters

3, 10, 11 and 124. Optical Physics, 3rd Edition, S.G.Lipson, H.Lipson, and D.S.Tannhauser, Cambridge University Press,

1995, Section 11.6.

9.2. Quantum Mechanics2

Time dependent perturbation theory: First order perturbation; mention of higher orders. Generaldiscussion of the electromagnetic interaction; interaction of atoms with electromagnetic radiation, energyshift and decay width. Scattering theory: Introduction, recapitulation of one-dimensional scattering andoverview. Lippmann-Schninger equation. The Born approximation and Eikonal approximation. Free particlestatusplane waves and spherical waves, method of partial waves. Two particle scattering. Low energyscattering and bound states. Resonance scattering.

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Relativistic quantum mechanics: Klein Gordon equation, plane-wave solutions, negative energy. Equationof continuity. The difficulties of the Klien-Gordon theory.

The Dirac equation: The free-particle Dirac equation in the Hamiltonian form. The algebra of Diracmatrices; Dirac-Pauli representation. The covariant form of the Dirac equation in the presence of anexternal electromagnetic field A. The Dirac -matrices and their algebra. Plane wave solutions of thefree-particle equation; the two-component form of the solution in the Dirac-Pauli representation, standardnormalisation of the solutions.

Spin of the Dirac particle: Non-conservation of the angular momentum operator L; the spin operator Sand the conservation of J L + S. Commutation relations involving L, S, J and J2. Helicity. A briefdiscussion of the hydrogen atom according to Dirac theory through simultaneous eigenstate of the operatorsH, J2, Jz and K

((2/h)S J (h/2)

)and the energy spectrum of the hydrogen atom. Negative energy

states and anti-particles.

Relativistic kinematics: Relativistic kinematics of scattering and reactions. The centre-of-mass frame.Transformation from the lab-frame to the centre-of-mass frame. Cross sections and asymmetries.

Field quantisation: The Lagrangean formalism for a field; Euler- Lagrange equations. Quantisation of theelectromagnetic field. Creation and annihilation operators. Fock states. Number representation. Quantisa-tion of Fermion field. Interacting fields. Perturbation theory and Feynman diagrams. Coulomb scattering.

References

1. J.J. Sakurai, Advanced Quantum Mechanics, Addison-Wesley, New Delhi, 19992. H Muirhead, The Physics of elementary particles, Pergamon, New York3. D Griffiths, Introduction to elementary particle physics, John-Wiley, New York, 1987

9.3. Solid State Physics

X-ray Crystallography: Crystalline state. Reference axes, equation of a plane, Miller indices, axial ratiosand zones. External symmetry of crystals; symmetry operations. Two and three dimensional point groups.Lattices; two dimensional lattices, choice of unit cell. Three-dimensional lattices; crystal systems and Bravaislattices. Screw and glide operations. Space groups; analysis of the space group symbol. Diffraction of X-rays by crystals: Laue equations. Reciprocal lattice. Bragg equations. Equivalence of Laue and Braggequations. Fourier analysis and inversion of Fourier series; Physical significance. Scattering from a unitcell; structure factors, scattering factors and systematic absences. Structure factors of the bcc and the fcclattices, Friedels law. Intensity data collection and corrections to be applied. Analysis and refinement(qualitative). Experimental techniques: Laue, powder, rotation, oscillation, Weissenberg and precessionmethods. Diffractometers.

Crystal growth: Crystal growth from melt and zone refining technique.

Liquid crystals: Morphology. The smectic (A-H), nematic and cholesteric phases. Birefringence, textureand X-ray studies in these phases. Orientational order and its determination in the case of nematic liquidcrystals.

Crystal lattice dynamics: Vibration of an infinite one-dimensional monatomic latticeFirst Brillouin Zone.Group velocity. Finite lattice and boundary conditions. Vibrations of a linear diatomic latticeoptical andacoustical branches relation.

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Formation of alloys: Interstitial and substitutional solid solutions, Hume-Rothery Rules-Electron Com-pounds. Bragg and Williams long-range-order theory.

Mossbauer effect: Application to lattice dynamics.

Magnetic properties of solids: Diamagnetism and its origin. Expression for diamagnetic susceptibility.Paramagnetism. Quantum theory of paramagnetism. Brillouin function. Ferromagnetism. Curie-Weisslaw. Spontaneous magnetisation and its variation with temperature. Ferromagnetic domains. Antiferro-magnetism. Two sublattice model. Susceptibility below and above Neel temperature.

Semiconductors: Intrinsic Semiconductors. Crystal structure and bonding. Expressions for carrier con-centrations. Fermi energy, electrical conductivity and energy gap in the case of intrinsic semiconductors.Extrinsic Semiconductors; impurity states and ionization energy of donors. Carrier concentrations and theirtemperature variation. Qualitative explanation of the variation of Fermi energy with temperature and im-purity concentration in the case of impurity semiconductors.

Semiconductor devices: Brief discussion of the characteristics and applications of tunnel diodes, photodi-odes, phototransistors, JFET, SCR and UJT.

References

1. Structure Determination by X-ray Crystallography, M.F.C.Ladd and R.A.Palmer,Plenum Press, New York.

2. X-ray Structure Determination, G.H.Stout and L.H.Jensen, MacMillan, New York.3. Crystals, X-rays and Proteins, D. Sherwood4. Solid State Physics, A.J Dekker, Macmillan, London.5. Introduction to Solid State Physics, 7th Edn., C Kittel, John Wiley, New York.6. Solid State and Semiconductor Physics, 2nd Edn. J.P.Mckelvey, 1966, Harper and Row, New York.7. Solid State Electronic Devices, 2nd Edn., B.G. Streetman, Prentice-Hall of India, New Delhi, 1983.8. The Physics of Liquid Crystals, 2nd Edn., P.G. De Gennes and J.Prost, Clarendon Press, Oxford, 1998.9. X-Ray Diffraction: its theory and applications, S.K.Chatterjee, Prentice-Hall of India, New Delhi,

1999.

9.4. Particle and Nuclear Physics

Properties of the nucleus: Nuclear radius-determination by mirror nuclei, mesic x-rays, electron scatteringand nuclear scattering methods (alpha,n). Nuclear moments: Spin, electric and magnetic moments. Relationbetween j and mu on the basis of single particle model. Determination nuclear magnetic moment by molecularbeam experiment, experimental determination of the magnetic moment of proton and neutron.

Nuclear decay modes: Beta decay. Beta ray spectrum, neutrino hypothesis, mass of the neutrino from betaray spectral shape, Fermis theory of beta decay, Kurie plot, ft-values and forbidden transitions. Methods ofexcitation of nuclei, Multipole transitions and internal conversion. Nuclear isomerism. Islands of isomerism.Resonance scattering of gamma rays. Mossbauer effect. Mass of the photon. Characteristic x-rays. Augereffect, Fluorescence yield.

Nuclear models: Liquid drop model - Weissackers formula - its application to (i) Stability of isobarsand (ii) Fission process. Shell model-single particle potentials, spin-orbit coupling and level scheme, Magicnumbers. Fermi gas model- estimation of well depth, level density, nuclear evaporation, the effect of Fermimomentum in particle production.

27

Interaction of nuclear radiation with matter: Energy loss due to ionization for proton-like particles andelectrons. Bethe-Bloch formula, Range-energy relations. Radiation loss of fast electrons, Fermis theoryof Bremstrahllung. Interaction of gamma and x-rays with matter. Photo effect, Compton effect, pairproduction.

Nuclear forces and elementary particles: General features of nuclear forces, spin dependence, chargeindependence, exchange character etc., Meson theory of nuclear forces - Yukawas theory, properties of pimesons-charge, isospin,mass, spin and parity, decay modes, meson resonances, strange mesons and baryons.CP violations in K-decay.

Particle interactions and families: Symmetries and conservation laws- classification of fundamental forcesand elementary particles. Associated particle production, Gellmann - Nishijima scheme, Eight- fold way,Quarks and Gluons, Colour, charm, beauty and truth. Quark dynamics. Idea of Grand Unified Theories.

References

1. Introductory Nuclear Physics, Halliday, Wiley, New York.2. Introductory Nuclear physics, Enge, Addison Wesley, New York.3. Introductory Nuclear physics, K.S.Krane, Wiley, New York.4. Introductory Nuclear Physics, Waghmare, M/S Oxford and IBH company, New Delhi5. Atomic and Nuclear Physics, Vol. 2, S.N.Ghoshal, S.Chand and Company, New Delhi6. Elementary-Particle Physics, Committee on Elementary-Particle Physics/ National Research Council,

Universities Press (India) Ltd., Hyderabad, 19987. Fundamental Particles- C.E. Schwartz8. Elementary Particles- C.N.Yang9. Elementary Particles- Frisch and Thorndike, Van Nostrand, New Jersey10. Fundamental Particles- K.Nishijima, Benjamin, New York11. Introduction to Particle Physics, M.P. Khanna, Prentice-Hall of India, New Delhi

9.5. Lab-9: Spectroscopy, Solid State and Nuclear Physics

Any eight of the following:

1. Determination of the paramagnetic susceptibility of the given salt by Quinckes method2. Study of mercury spectrum by superposing it on brass spectrum3. Sodium spectrum analysis by using Edser-Butler fringes4. Temperature coefficient of resistance of a thermistor5. Analysis of the powder X-ray photograph of a simple cubic crystal6. Thermionic work-function of a metal (Richardson-Dushmann formula)7. Study of the Raman effect in a liquid8. Determination of the Curie temperature of a ferromagnetic material9. Half-life of Indium-11610. Resolution of a NaI(TI) scintillation spectrometer11. Compton scattering determination of the rest energy of an electron12. Beta absorption studies13. Dekatron14. Gamma-ray absorption studies

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Semester-10

10.1. Modern Biology for Physicists

Cell biology and biochemical methods: Cell division and cell cycle events, sub-cellular fractionation,principle and methodology of chromatography, electrophoresis, ultracentrifugation and tracer techniques.

Structure and function of proteins and enzymes: Amino acids, peptides. Proteins: structure and function.Enzymes: general properties, kinetics, mechanism of action and regulation of activities.

Bioenergetics and metabolism: Role of ATP, biologic oxidation, respiratory chain and oxidative phospho-rylation. Overview of intermediary metabolism, integration of metabolism.

Structure, function and replication of informational macromolecules: Nucleotides, nucleic acidic struc-ture and function. DNA organisation, replication and repair. RNA synthesis, processing and modification.Protein synthesis and the genetic code, regulation of gene expression, recombinant DNA technology.

Biochemistry of extracellular and intracellular communication: Membranes: Structure, assembly andfunction. Harmone action: general information, mechanism of peptide and steroid hormone action, signifi-cance of over and under production.

Special topics: Vitamins, glycoproteins, the extracellular matrix, muscle and cytoskeleton, plasma proteins,immunoglobulins, blood coagulation, metabolism of xenobiotics, cancer, cancerogens and growth factors,biochemical and genetic basis of disease, biochemical basis of neuropsychiatric disorders.

References

1. Molecular Biology of the Cell, B.Alberts, D.Bray, J.Leurs, M.Raff, K.Roberts and J.D.Watson, 19942. Molecular Cell Biology, H.Lodish, D.Baltimore, A.Berk, S.L.Zipensky P.Matsudaira and J.Darnell,

19953. Biochemistry, L.Stryer, W.H.Freeman, New York, 19954. Biochemistry, D.Voet and J.G.Voet, John-Wiley, New York, 19955. Principles of Biochemistry, A.L.Lehringer, D.V.Nelson and M.M.Cox, CBS Publications, Delhi, 19936. Principles of Biochemistry, G.L.Zubay, W.W.Parson and D.E.Vance, W.C.Brown Publishing, Dubuque,

Iowa, 19957. Practical BiochemistryPrinciples and Techniques, K.Wilson and J.Walker (Editors), Cambridge Uni-

versity Press, Cambridge, 1994

MO-1: Riemannian Geometry and General Theory of Relativity

Affine manifolds: Levi-Civita transport and affine connection. Flat and non-flat affine manifolds. Coderiva-tives. Transformation law and other properties of the affinity. Tensors fields on a curve and intrinsic deriva-tives. Geodesics. Successive co-differentiation and the Riemann tensor. Local geodesic coordinates.

Geometry of spacetime: Space-time manifold. Spacetime metric, signature. Metric tensors and associatetensors. The metric affinity. Variational principle for geodesics. (The case of timelike geodesic only need bediscussed.) The curvature tensor and its algebraic properties. Enumeration of the number of independentnon-zero components of the curvature tensor. The necessary and sufficient condition for flatness. (Proofof sufficiency not expected.) Contraction of the curvature tensor. The tensors of Ricci and Einstein. TheBianchi identity and its contracted form.

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Orthonormal tetrads: Orthonormal tetrads (ONTs) in spacetime. Lorentz transformations as transfor-mations connecting different ONTs at an event. Construction of a locally inertial coordinate systems at anevent of spacetime.

Einstein equations: The principles of equivalence and general covariance. Gravitational field equations ofEinstein. The weak field, slow velocity, approximation and the identification of the corresponding Newtoniangravitational potential and the universal constant in the equation.

The Schwarzschild solution: The solution. Geodesics of the Schwarschild field. Advance of planetaryperihelia, light bending, time delay and gravitational redshift in the Schwarzschild field.

A brief qualitative account of black holes, gravitational waves and gravitational lensing.

References

1. The Classical Theory of Fields, 4th. Edn., Pergamon Press, 19852. General Relativity, R.M.Wald, The University of Chicago Press, Chicago, 19843. A First Course in General relativity, B.F.Schutz, Cambridge University Press, Cambridge, 1985

MO-2: Physical Properties of Solids

Imperfections in solids: Different types of imperfections and their energy of formation. Diffusion in metals.Kirkendall effect. Ionic conductivity in pure and doped halides. Colour centres, excitons, photoconductivity,traps, space charge effects, crystal counter. Photographic process.

Dislocations: Shear strength of single crystals. Dislocations-Burgers vector. Stress fields of dislocation,Low-angle grain boundaries. Dislocation and crystal growth. Whiskers.

Free electron theory of metals: Boltzmann transport equation, Sommerfelds theory of electrical con-ductivity, mean free path in metals, temperature dependence of resistivity on temperature and impurities.Matthiessens rule. Electron-photon collisions. Thermal conductivity of insulators, Umklapp processes. Elec-trical conductivity of metals at high frequencies. Plasma frequency. Transparency of alkali metals to UVradiation. Anomalous skin effect. Plasmons. Field enhanced emission, Schottky effect. Hall effect andmagnetoresistance in metals. Cyclotron frequency.

Band theory of Solids: Bloch theorem, Bloch functions, periodic potentials, reciprocal lattice, periodicboundary conditions, density of states, Brillouin zones, nearly free electron approximation, approximate so-lution near a zone boundary, tight-binding approximation, application to square and cubic lattices. Constantenergy surfaces, Fermi surfaces. Brillouin zones in square lattice. Overlapping of bands. Soft x-ray emissionspectra. Explanation of Hume-Rothery rules in binary alloys in terms of Brillouin zones

Superconductivity: Elementary ideas of BCS theory. Cooper pairs, energy gap, Meissner effect, fluxquantisation, Josephson tunnelling, Josephson junction. Elements of theory for DC and AC bias. QuantumInterferometers. High Tc Superconductors.

Luminescence: General remarks, Excitation and Emission. Franck-Condon principle. Decay mechanisms-Temperature dependent and independent decays. Thermo-luminescence and glow curve, electro-luminescence.Gudden-Pohl effect, carrier injection luminescence.

Dielectric properties of solids: Polarisation. Macroscopic electric field. Depolarisation field. Localelectric field at an atom. Lorentz field. Field of dipoles inside cavity. Dielectric constant and polarizability,Clausius-Mossotti relation. Electronic, ionic and orientational polarizabilities. Polarisation catastrophe.Dipole orientation in solids. Debye relaxation time, relaxation times in solids, complex dielectric constantsand loss angle. Classical theory of elctronic polarization and optical absorption.

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Ferro electricity: Basic properties of ferroelectric materials. Classification of ferroelectric crystals. The-ories of Barium titanate. Displasive transition, thermodynamics of ferroelectric phase transitions. Londontheory of the phase transition. Dielectric constant near the curie point. LST relation and its implication.Ferroelectric domains. Antiferroelectricity.

Elastic constants of crystals: Analysis of elastic strains and stresses. Elastic compliance and stiffnessconstants, applications to cubic crystals and isotropic solids. Elastic waves and experimental determinationof elastic constants.

Magnetic properties of solids: Ferromagnets. Ground state of the Heisenberg ferromagnet. Ground stateof the Heisenberg antiferromagnet. Low temperature behaviour of the Heisenberg ferromagnet; spin wavesin one-dimension, quantisation of spin waves, thermal excitation of magnons, Blochs T 3/2 law for variationof magnetisation.

Paramagnetic relaxation: Phenomenological description; complex susceptibility. Casimir and Dupresthermodynamical theory of spin lattice relaxation, spin-spin relaxation.

Magnetic resonance: Elements of theory of NMR, Blochs equations, solutions for the steady state caseand that of the weak RF field, power absorption, change of inductance near resonance, saturation at highRF power. Dipolar line width in a rigid lattice. Ferromagnetic resonance; elements of the theory.

Behaviour of solids under high pressures: changes in mechanical, electrical and other physical properties

Thin Films: Preparation of organic and metallic thin films. Measurement of the thickness of the thin films.Electrical, mechanical and optical properties of thin films. Some applications of thin films.

References

1. Solid State Physics, A.J Dekker, Macmillan, London.2. Introduction to Solid State Physics, 7th Edn., C Kittel, John Wiley, New York.3. Solid State and Semiconductor Physics, 2nd Edn. J.P. Mckelvey, 1966, Harper and Row, New York.4. Solid State Electronic Devices,2nd Edn., B.G. Streetman, Prentice-Hall of India, New Delhi, 1983.5. Fundamentals of Solid State Physics, B.S. Saxena, R.C. Gupta and P.N.Saxena, Pragathi Prakashana,

Meerut.6. Solid State Physics, H.Itach and H.Luth, Narosa, New Delhi7. Solid State Physics, S.O. Pilai, Wiley Eastern Ltd.8. Physical Properti