UNIVERSITY OF HYDERABAD

M.Sc. (Physics)

Course Structure and Course details

(Approved by the School Board in February, 2006)

School of PhysicsM.Sc. (Physics) Programme

Semester I Total No. of Credits : 26Course No. Name of the Course Contact Hours and Credits

Classroom Lectures

Experiments in Laboratories

Total Credits

PY401 Mathematical Methods – I 4 -- 4PY402 Classical Mechanics 4 -- 4PY403 Electromagnetic Theory – I 4 -- 4PY404 Electronic Circuits Theory 4 -- 4PY405 Computational Methods 2 4 4PY406 Electronic Circuits Laboratory 2 8 6

Semester II Total No. of Credits : 26Course No. Name of the Course Contact Hours and Credits

Classroom Lectures

Experiments in Laboratories

Total Credits

PY451 Mathematical Methods – II 4 -- 4PY452 Quantum Mechanics - I 4 -- 4PY453 Electromagnetic Theory – II 4 -- 4PY454 Statistical Mechanics 4 -- 4PY455 Signals & Systems 2 -- 2PY456 Digital Electronics Laboratory 2 4 4PY457 Modern Physics Laboratory 2 4 4

Semester III Total No. of Credits : 26Course No. Name of the Course Contact Hours and Credits

Classroom Lectures

Experiments in Laboratories

Total Credits

PY501 Quantum Mechanics – II 4 -- 4PY502 Introduction to Particle Physics 4 -- 4PY503 Introduction to Solid State Physics 4 -- 4PY504 Introduction to Laser Physics 4 -- 4PY505 Nuclear Physics 2 -- 2PY506 Solid State Physics Laboratory 2 4 4PY507 Laser Physics Laboratory 2 4 4

Semester IV Total No. of Credits : 26Course No. Name of the Course Contact Hours and Credits

Classroom Experiments in Total

Lectures Laboratories CreditsSpecial Paper – I 3 -- 3Special Paper – II 3 -- 3Special Paper – III 3 -- 3Optional Paper – I* 3 -- 3Optional Paper – II* 3 -- 3

PY551 Nuclear Physics Laboratory 2 4 4PY552 Microwave Laboratory 2 4 4

• One of the optional papers only

SpecializationsCourse No. Name of the Course Contact Hours and Credits

Classroom Lectures

Experiments in Laboratories

Total Credits

A Particle PhysicsPY553 Field Theory & Quantum Electro-

dynamics3 -- 3

PY554 General Relativity & Gravitation 3 -- 3PY555 Particle Physics 3 -- 3

B Solid State PhysicsPY556 Superconductivity 3 -- 3PY557 Magnetism 3 -- 3PY558 Semiconductor Physics 3 -- 3

C Laser Physics and Quantum OpticsPY559 Elements of Non-linear Optics 3 -- 3PY560 Elements of Quantum Optics 3 -- 3PY561 Optical Resonance 3 -- 3

D ElectronicsPY562 Microprocessors and Microcontrollers

Theory3 -- 3

PY563 Microprocessors and Microcontrollers Laboratory

-- 8 3

PY564 Advanced Digital Signal Processing Theory

3 -- 3

Optional PapersCourse No. Name of the Course Contact Hours and Credits

Classroom Lectures

Experiments in Laboratories

Total Credits

PY571 Lie Groups & Lie Algebra 3 -- 3

PY572 Dynamical Systems and Chaos 3 -- 3PY573 Probes of Condensed Matter 3 -- 3PY574 Physics of Materials 3 -- 3PY575 Low Temperature Techniques 3 -- 3PY576 Advanced Solid State Physics

Laboratory-- 8 3

PY577 Advanced Statistical Mechanics 3 -- 3PY578 Many Body Theory 3 -- 3PY579 Ferroelectrics & Electroceramics 3 -- 3PY580 Liquid Crystals 3 -- 3PY581 Non-linear Spectroscopic Techniques 3 -- 3PY583 Opto electronics 3 -- 3PY584 Optical Cooling 3 -- 3PY585 Cavity Quantum Electrodynamics 3 -- 3PY586 Coherence & Quantum Interference 3 -- 3PY587 Nano-technology Theory & Lab. 2 4 3PY588 MEMS Theory & Laboratory 2 4 3PY589 Integrated Optics Theory & Lab. 2 4 3PY590 Semiconductor Physics Theory 3 -- 3PY591 Advanced Quantum Mechanics and

Many Body Theory3 -- 3

PY592 Advanced Computational Techniques 3 -- 3PY593 Ultra-fast Phenomena 3 -- 3PY594 Phase Transitions and Critical

Phenomena3 -- 3

PY595 Nanostructuring by various problems (lasers, ion beams, sputtering etc.)

3 -- 3

PY596 Project * -- -- 6• Project is compulsory.

COURSE DESCRIPTION OF VARIOUS COMPULSORY/CORE COURSES & OPTIONAL COURSES

Four numbers (a,b,c,d )followed immediately after the course title refer to number of lectures (a), number of tutorials (b), number of laboratory hours (c) per week, and number of total contact hours per week. Each hour is a contact hour of 50 minutes.

PY401 Mathematical Methods – I (4, 0:4)

Fourier series and Fourier transforms, their properties & applications. Definition and properties of Dirac delta function.

The method of separation of variables for partial differential equation, boundary value problems involving use of Fourier expansion.

Linear ordinary differential equations with constant coefficients and the Euler equation. The Frobenius method of series solution. Fuch’s theorem. Polynomial Solutions.

Geometrical representation of complex numbers. Functions of complex variables. Propertie3s of elementary trigonometric and hyperbolic functions of a complex variable. Differentiation, Cauchy-Riemnann equations. Properties of analytical functions. Contours in complex plane. Integration in complex plane. Cauchy theorem. Deformation of contours. Cauchy integral representation. Taylor series representation. Isolated and essential singular points. Laurent expansion theorem. Poles. Residues at an isolated singular point. Cauchy residue theorem. Applications of the residue theorem.

Laplace transform & applications.

Recommended books :

1. Mathematics for Physicists Dennery & Kryzywicki2. Ordinary differential equations R. L. Rabenstein3. Complex Variables & Applications R. V. Churchill4. Partial Differential Equation for Scientists G. Stephenson

PY402 Classical Mechanics (4, 0:4)

A brief and quick review of Newtonian mechanics of a particle and a system particles.Lagrangian Formalism : force, potentials, conservative systems constrains, generalized coordinates. Lagrange equations, variational principles, conservation theorems and symmetry properties. Lagrangian of a charged particle in an electromagnetic field. Two body central force problem, scattering due to simple potentials like central force fields.Hamiltonian formalism, conjugate momenta, conservation laws, Hamiltonian of a charged particle in electromagnetic field.Poisson brackets and their properties, equation of motion. Canonical transformation.A brief introduction to the Hamilton-Jacobi’s Theory and action angle variables.Theory of small oscillations, normal modes of the system.

The kinematics of rigid body motion, infinitesimal rotations, the Coriolis force, rigid body equations of motion.Recommended books :

1. Classical Dynamics J. B. Marion2. Classical Mechanics H. Goldstein3. Mechanics Landau-Lifshitz4. Classical Mechanics A. K. Raichaudhuri5. Classical Dynamics Jog & Rana

PY403 Electromagnetic Theory – I (4, 0:4)

Maxwell’s equations for electrostatics and magnetostatics in differential and integral form.

Electrostatic potential and electrostatic field due to point charges and continuous charge distributions. Electrostatic field energy. Boundary value problems and their solutions by separation of variables. Method of images and Green functions. Multipole expansion. Electric dipole and quadupole moments. Dielectric materials. Polarization. Maxwell’s equations for electrostatics in presence of dielectric materials. Boundary value problems in presence of dielectrics.

Introduction to vector and scalar potentials in electrostatics. Gauge transformations, magnetic field and vector potential for simple steady current configurations. Force and torque on current carrying conductors. Magnetic multipole expansion.

Dia, para and ferro-magnetic materials, Maxwell’s equations in presence of magnetic materials.

Time varying fields. Faraday’s Laws of induction. Maxwell’s equations of electrodynamics. Magnetic field energy. Self and mutual inductance.

Recommended books :

1. Introduction to Electrodynamics Griffiths2. Electrodynamics of continuous media Landau & Lifshitz3. Classical Fields Landau & Lifshitz

PY404 Electronics Circuit Theory (4, 0:4)

Network theorems. A. C. Equivalent Circuits of networks with active devices.

Power Supplies : Half-Wave, Full-Wave and Bridge rectifiers with Capacitive input, Inductance input and PI filters. Regulated power supplies : Shunt regulated power supplies using zener diodes, Series regulated power supply. I. C. Voltage regulators.Transistor amplifiers : The CE, CB and CC configurations. Class A, Class B and Class C amplifiers. Low-frequency amplifiers. The transistor hybrid model and the h-parameters for a transistor. Conversion formulae for the h-parameters of the different transistor configurations. Analysis of a transistor CE amplifier at low frequencies using h-parameters. The CE amplifier with unbypassed emitter resistor. The emitter follower at low frequencies. The emitter-coupled differential amplifier and

its characteristics. Low frequency power amplifiers. The push-pull and the complementary - symmetry power amplifiers. Transistor biasing, Self-bias and thermal stability.

The BJT at high frequencies – the hybrid – model. Analysis of CE amplifier at high frequencies. Single stage CE amplifier and the gain-bandwidth product. Cascaded amplifiers. The emitter follower at high frequencies.

The field effect transistor and its small signal model. The CS and CD amplifiers at low frequencies. Biasing the FET. The CS and CD amplifiers at high frequencies.

Feedback : The Gain of an amplifier with feedback. General characteristics of negative feedback amplifiers. Stability of feedback amplifiers, The Barkhaussen Crieteria. Grain and Phase margins. Compensation. Sinusoidal oscillators: RC oscillators – The Phase shift and the Wien’s bridge oscillators. LC oscillators. Frequency stability and the crystal oscillators.

Operational amplifiers : Characteristics of an ideal operational amplifier. Applications of operational amplifiers – Inverting and Non-inverting amplifiers. Summing circuits, integration and Differentiation. Waveform generators.

Recommended books :

1. Integrated Electronics Maillman and Halkias2. Introduction to Operational Amplifiers

PY405 Computational Methods (2, 4:4)

1. Roots of algebraic and transcendental equations : One point and two-point iterative methods Such as bisection method, inverse interpolation and Newton Raphson methods.

2. Matrix operations and simultaneous linear equations : Matrix addition, multiplication and inversion. Solution of simultaneous linear equations by matrix inversion methods.

3. Interpolation : Linear interpolation, Lagrangian interpolation, Newton’s interpolation (different forms).

4. Integration : Newton-Cotes formulae, Gauss quadrature.

5. Ordinary Differential equations : Initial value problem Taylor’s algorithm, Euler’s methods, Runge-Kutta, and Predictor-corrector methods.

Recommended books :

1. Introduction to Numerical Methods T. R. McCalla2. Numerical Methods that work F. S. Acton3. An Introduction to Numerical Analysis K. E. Atkinson4. Numerical Recipes W. H. Press et.al

PY406 Electronics Circuit Laboratory (2, 8:6)

Diode Applications – I : Power supplies – Bridge rectifiers with capacitive input filters. Shunt Voltage regulator using zener diode.

Diode Applications – II : Clipping and Clamping circuits. BJT characteristics. Determination of h-parameters in the CE configuration using the

measured input and output characteristics of a BJT (e.g.2N 2218) Common Emitter Amplifier with and without feedback. Common Source and Common Drain Amplifiers using JFET. RC Oscillators : Phase shift oscillator using RC ladder network as the phase shifting

network; Wien’s Bridge Oscillator. Emitter Coupled Differential Amplifier using BJT’s. Multivibrators – Bistable, Monostable and Free Running multivibrators using BJT’s (e.g.2N

2218). Op-Amp (741) characteristics : V io, Ib, Vol, CMRR, Slew Rate. Applications of Op-amps :

inverting Amplifier, Unity Gain Buffer, Summing Amplifier. 555 IC timer. Free Running and Monostable Multivibrators, Sawtooth wave generator. Series Dissipative Voltage Regulator using 723 IC. Series Switching Voltage Regulator using 494 IC. Tuned High Frequency Amplifiers : RF and IF amplifiers. High Frequency Oscillators : Colpitts and Hartley Oscillators.

PY451 Mathematical Methods – II (4, 0:4)

Groups, fields, vector spaces, Linear dependence. Basis subspace, Dimension, Linear functions, Linear operators, Inverse and rank of an operator.

Eigenvalues and Eigenvectros. Matrix representation, Change of basis.

Norm and Inner product. Cauchy-Schwarz. Inequality. Orthogonality and completensess. Hermitian, unitary, projection operators. Positive operators. Change of orthonormal basis. Orthogonalization procedure.

Direct sum, quotient and tensor product of vector spaces.

Definitions and examples of physically important finite groups. Point groups, multiplication table, subgroups, cyclic groups, center, classes, cosets, Lagrange Theorem. Representations of finite groups, Irreducible representation characters, orthogonality theorem, Schur’s character table. Simple applications to small oscillations and selection rules in molecular spectra.

Recommended books :

1. Mathematics for Physicists Dennery & Kryzywicki2. Complex Variables & Applications R. V. Churchill3. Linear Vector Spaces R. R. Halmos4. Theory of Finite Groups L. Jansen and M. Boon

PY452 Quantum Mechanics – I (4, 0:4)

Review of linear algebra and introduction to Hilbert space. Dirac Bra-Ket notations, Fock representation

Schrodinger wave equation. Ehrenfest theorem, stationary states and their properties. Postulates of Quantum Mechanics. The general solution of wave equation and its applications to Harmonic oscillator, delta function potential, potential well in three dimensions. Hydrogen atom and rigid rotator. Wave packets and the uncertainly principle. General formulation of uncertainly principle. Time development of wave packets.

Angular momentum. Commutation relations, eigen-functions of the angular momentum operators, matrix representation of angular momentum operators.

Introduction to perturbation theory.

Scattering Theory, Central force problem, partial wave analysis Born’s approximation, optical theorem bound states and resonances. Schrodinger and Heisenberg pictures.

Recommended books :

1. Quantum Mechanics L. Schiff2. Quantum Mechanics E. Merzbacher3. Practical Quantum Mechanics S. Flugge4. Quantum Mechanics Mathews and Venkatesan5. Quantum Mechanics M. P. Khanna6. Principles of Quantum Mechanics P. A. M. Dirac7. Lectures on Quantum Mechanics G. Baym

PY453 Electromagnetic Theory – II (4, 0:4)

Maxwell’s equations of electrodynamics. Time dependent scalar and vector potentials. Gauge transformations. Coulomb and Lorentz gauges. Wave equation. Plane wave solutions. Polarization. Poynting’s theorem. Conservation of energy. Momentum and angular momentum of electromagnetic fields.Reflection, refraction and dispersion. Propagation in conductors and plasmas. Skin effect. Propagation in Waveguides.

Retarded potentials. Lienard-Wiechert potentials. Radiation from a moving point charge and oscillating electric and magnetic dipoles. Multipole expansion for radiation fields.

Introduction to special theory of relativity. Lorentz transformation. Transformations of electromagnetic fields under Lorentz transformations.

Recommended books :

1. Introduction to Electrodynamics Griffiths2. Electrodynamics of continuous media Landau & Lifshitz3. Classical Fields Landau & Lifshitz4. Classical Electodynamics J. B. Marion

PY454 Statistical Mechanics (4, 0:4)

Basic Statistical ideas : Probability concepts, states of classical and quantum systems.Isolated systems : Microcanonical ensemble, statistical entropy, most probable state. Systems in thermal and diffusive contact. Conditions for equilibrium. Canonical and grand canonical ensemble, and partition functions.Thermodynamics : Extensive and intensive variables, laws of thermodynamics, various thermodynamic potentials and their connection with partition functions.

Ideal Fermi and Bose gases : Distribution functions, classical limit. Electron gas in a metal. Black body radiation. Debye theory. Bose Einstein Condensation.

Elementary ideas about phase transitions of different kinds. Examples of some phase transitions.

Recommended books :

1. Thermal Physics C. Kittel2. Statistical Physics L. D. Landau and E. M. Lifshitz3. Problems in Thermodynamics and

Statistical Physics P. T. Landsberg (Ed.)4. Introduction to Statistical Mechanics F. Reif

PY455 Signals & Systems (2, 0 : 2)

Basic Continuous-time and Discrete-time signals; LTI Systems and their properties

Time-domain analysis of LTI Systems : Convolution of continuous-time and discrete-time signals; Impulse response and convolution representation of continuous-time and discrete-time signals; modeling and realization of systems described by linear differential and difference equation with constant coefficients.

Frequency domain analysis of continuous time LTI systems : Response of systems to complex exponential signals, Fourier series representation of periodic signals Fourier Transform of a-periodic signals, properties of the Fourier Transform, Frequency response of systems described by linear differential equations with constant coefficients and Form-II realization, Analysis of First and Second order systems.

Laplace Transform analysis of continuous time signals : The Laplace Transform, its region of convergence, properties and its relation to FT; System transfer function, Laplace transform analysis of systems described by linear differential equations with constant coefficients, pole-zero plots and their interpretations.

*Analysis of Ideal filters, filter transformations and their realization-Butterworth, Chebychey, elliptic and inverse filters

Frequency domain analysis of discrete-time systems : Discrete time Fourier series and Fourier Transform and their properties;*Discrete Fourier Transform (DFT), properties of DFT, FFT algorithms

*z-Transforms: Definition and properties, rational z-transforms and their regions of convergence, inverse z-transform, z-transform properties, System response function for systems characterized by linear difference equations with constant coefficients.Sampling: The sampling theorem and aliasing, interpretation in frequency domain*Reconstruction of signals from its samples using interpolating filters-ideal low-pass, zero- and first-order hold.*Frequency domain sampling, decimation and interpolation*Realization of discrete-time systems for sampled signals from continuous time specifications.

Probability, random signals, spectral densities, white noise and 1/f noise, separation of signals from noise.

Signals and Systems: A. V. Oppenheim and A. S. Willsky, Prentice HallDigital Signal Processing- A Computer-based Approach: S. K. Mitra, McGraw-HillSignals Systems and Transforms: C. L. Phillips and J. M. Parr, Prentice HallIntroduction to Signals and Systems: D. K. Lindner, McGraw-HillIntroduction to Digital Signal Processing: Johny R. Johnson

*Optional at the discretion of the instructor, if time permits

PY456 Digital Electronics Laboratory (2+2=4)

Course Description and Objectives:

The objective of this course is to provide an understanding of digital electronics through both analysis/design and lab investigation. Digital topics include digital signals, number systems, Boolean algebra, logic gates, combinational logic, flip-flops and sequential logic, counters, registers, DAC/ADCs. The course will have 2 hours of lecture each week accompanied by a 4 hour lab.

Course Program

Digital computers, number systems, Arithmetic operations, decimal codes, Gray codes, alphanumeric codes Combinational logic circuits, binary logic and gates, Boolean algebra, Standard forms, Two-level circuit optimization, functions of two variables, exclusive-OR operator.

Combinational logic design: design concepts, Design procedure, Combinational functions and circuits, Binary adders (half and full adder), Binary subtraction (half and full subtraction), binary adder-subtractors, Decoder, encoder, multiplexers, demultiplexer.

Sequential circuits: latches, Flip-flops: R-S, J-K, Master slave J-K, D type and T type Flip Flop. Sequential circuit design, Registers, Shift registers, Synchronous Counters, Asynchronous Counters, Arbitrary sequence counter design and construction.

Data Converters: Analog to Digital data converters, Digital to analog data converters.

Any other topic (eg. Logic families, microprocessors) at the discretion of the course instructor.

References:

Digital Logic and Computer Design, M. Morris Mano, Prentice-Hall India Pvt. Ltd.Digital Electronics: Fundamental Concepts and Applications, C. E. Strangio, PHI.

Laboratory:

Universal Gate, adder/subtractor, decoder, multiplexer, BCD-to-7 segment decoder/driver, 555 timer/clock, J-K flip-flop, serial counter, parallel up/down counter, decade counter, ring counter, arbitrary sequence counter design & implementation.

Any other experiment (eg. Microprocessor applications, project) at the discretion of the course instructor.

PY457 Modern Physics Laboratory (2,4:4)

A. Optics

1. Interference (Fabry-Perot)2. Fraunhoffer Diffraction and acousto-optic experiments3. Polarisation (Brewster angle, QW plate, Half wave plate)4. Photo electric effect5. Ionization potential (Optional)6. Atomic and Molecular Spectra (Optional)

B. Properties of matter

1. Specific heat of graphite2. Band gap of a semiconductor3. Magnetic susceptibility by Guoy method4. Vacuum system-operation & thin film deposition5. Crystal growth and morphological study (Optional)6. Colour centres and photoconductivity of alkali halides (Optional)

C. Demonstration Experiments

1. Interference (Biprism)2. Fresnel diffraction3. Holography4. Fibre Optics

PY501 Quantum Mechanics – II (4, 0:4)

Perturbation methods. Rayleigh-Schrodinger perturbation theory, degenerate case, applications, variational methods. WKB approximation. Time dependent perturbation theory, Fermi’s Golden rule. Semiclassical radiation theory, interaction of charged particles with electromagnetic fields, polarizability of a system, Photo-electric effect, Einstein’s A, B coefficients.

Spin. Stern Gerlach experiment, Pauli’s two component equation, addition of angular momenta. Identical particles, symmetrization postulate, Bose and Fermi-statistics, Pauli exclusion principle.

Helium atom, Spin in a time dependent magnetic field, Hartree-Fock method. Symmetry in quantum mechanics, space and time displacements, rotations, space inversion, time reversal, Spin-orbit coupling, j-j coupling, Zeeman effect.

Quantum mechanics of molecules, Born-Oppenheimer approximation.

Relativistic Quantum Mechanics, Klein Gordon equation, Dirac equation, properties of Dirac Matrices, positive and negative energy states. Free Dirac particle in an external electro-magnetic field.

Recommended books :

1. Quantum Mechanics L. Schiff2. Quantum Mechanics E. Merzbacher3. Practical Quantum Mechanics S. Flugge4. Quantum Mechanics Mathews and Venkatesan5. Quantum Mechanics M. P. Khanna6. Principles of Quantum Mechanics P. A. M. Dirac7. Lectures on Quantum Mechanics G. Baym

PY502 Introduction to Particle Physics (4, 0:4)

Special theory of relativity and kinematics.

Classification of fundamental interactions and elementary particles. Yukawa’s proposal on meson exchange.

Symmetries and conservation laws.

Nother’s theorem in classical mechanics, (ii) continuous space time symmetries and associated conservation laws of momentum, energy, angular momentum. Lorentz invariance, (iii) Symmetries in quantum mechanics. Discrete Symmetries, Parity, Charge conjugation and time reversal (iv) Examples of determination of intrinsic quantum numbers, mass and spin, (v) Charge independence of nuclear forces, isospin and strangeness. Application of isospin invariance to pion nucleaon scattering, (vi) Starngeness charm and other additive quantum numbers, (vii) Resonance and their quantum numbers with special reference to pion nucleaon scattering. Gell Mann Nishijima formula.

Violation and symmetries : Isospin violation in electromagnetic interactions, Parity non-conservation in weak interactions, CP violations and KoKo system.

Experimental techniques : Cycolotron, synchrotron, linear accelerators, colliding beam experiments, intersecting storage rings and stochastic cooling. Detectors for photons, leptons and hadrons.

Recommended books :

1. Introduction to High Energy Physics Perkins2. Introduction to Particle Physics Griffiths3. Invariance Principles & Elementary Particles Sakurai4. Introduction to Particle & Nuclear Physics T. Ferbel and A. Das

PY503 Introduction to Solid State Physics (4,0:4)

Chemical binding, crystal structure, X-ray diffraction, reciprocal lattice and Brillouin zones.Lattice vibrations, phonons, thermal properties.

Free electron gas, Band theory of solids, Semiconductors, Transport properties.

Magnetism : Dia-, para-, ferro-, antiferro and ferrimagnetism.

Superconductivity : Experimental survey, Thermodynamics of superconductors, London’s equations. High lights of BCS theory results.

If time permits : Elastic properties, Dielectric and Ferroelectric materials, Optical properties of solids.

Recommended books :

1. Introduction to Solid State Physics C. Kittel2. Solid State Physics J. S. Blakemore3. Principles of Solid State Physics R. A. Levy4. Principles of the Theory of Solids J. Ziman

PY504 Introduction to Laser Physics (4, 0:4)

Laser and its applications (introductory).

General Physical principles behind amplification : Spontaneous emission. Stimulated effects. Lasing action Role of feedback (cavity). Comparison with blackbody radiation.

Cavity design : Caussian beam in spherical mirror cavity, longitudinal and transverse modes. Losses and Q-factor.

Different Laser Systems : Gas Lasers, solid state, free electron, liquid state and excimer lasers. Operation principle and design specifics. Output characteristics.

Modelocking, relaxation oscillations and Q-switching.

Single mode laser theory : (a) Rate equation, (b) Semiclassical theories. Ideas about linewidths.

Recommended books :

1. An Introduction to Laser & their Applications O’Shea, Callen & Rhodes2. Introduction to Laser Physics K. Shimoda3. Laser Physics M. Sargent, M. O. Scully & W. E. Lamb4. Lasers Siegman5. Lasers Svelto6. Quantum Electronics Yariv

PY505 Nuclear Physics (2,0:2)

Properties of Nuclear forces-deutron problem, n-p scatteringNuclear Shell Model and Collective ModelAlpha Decay-Systematics and theoryBeta Decay-Fermi Theory, Selection RulesGamma Decay and Internal Conversion, Selection rulesNuclear Reactions-Cross Sections, Compound NucleusNuclear Fission and Fusion

Recommended books :

1. Introductory Nuclear Physics Kenneth S. Krane, John Wiley (1988)2. Physics of Nuclei and Particles E. Segre3. Elements of Nuclear Physics W. E. Burcham, Longman (1986)4. An Introduction to Nuclear Physics W. N. Cottingham and D. A. Greenwood

PY506 Solid State Physics Laboratory (2,4:4)

(6-8 Experiments from the following ones)

1. Temperature measurement : thermistor, diode & Pt. Resistor.2. Electrical resistivity of Cu & Fe.3. Determination of unit cell symmetry and lattice parameter by powder and Laue methods.4. Determination of carrier concentration and their sign in Ia Semiconductor at room temperature

by Hall effect and magnetoresistance measurements.5. Determination of the defect activation energy in an alkali halide crystal by measuring its ionic

conductivity as a function of temperature.6. Dielectric constant and dielectric loss measurements as functions of temperature and frequency

to study structural phase transitions.7. Study of order-disorder transition in β-brass by heat capacity measurements.8. Superconductivity in high Tc superconductors.9. Electrical resistivity of metallic glasses : nonmagnetic & magnetic10. Thermoelectric power of metallic glasses : nonmagnetic & magnetic.11. Optical spectra of thick semiconducting films.

PY507 Laser Physics Laboratory (2,4:4)

A minimum of 6 experiments to be performed.

Measurement of longitudinal and transverse modes of He-Ne laserBerry’s phaseMeasurement of wavelength of He-Ne laser radiation by a meter scaleElectro-optic effect: (a) Induced anisotropy in nitrobenzene, (b) In KDP and LiNbO3 crystalsSecond harmonic generation in crystalsSelf-focussing in liquidsIntegrated optics: Surface phonon generation, measurement of film properties, planar optical wave- guide characterization by coupling through a prism

Amplitude modulation of light: Application of light as a carrier wave for acoustic frequenciesLaser Doppler Anenometry: To obtain velocity profile of flow in a pipe and verify Poiseuille formula.

PY561 Nuclear Physics Laboratory (2,4:4)

Minimum of 6 experiments to be performed

1. Geiger Muller Counter-Counting Curve. Verification of Inverse Square Law. Dead time of detector using Split Source Method. Counting Statistics and Error prediction. Half Life.

2. Gamma Spectroscopy using Single Channel Analyser-Differential and Integral Pulse Height Spectra of Cs-137. Detector Resolution.

3. Gamma Spectroscopy using Multichannel Analyser-Energy Calibration and Identification of unknown source. Resolution. Spectrum Analysis. Determination of Activity. Peak Integration. Stripping and Background Subtraction.

4. Mass Attenuation of Gamma Radiation in Al5. Mass attenuation Coefficient of Beta Radiation of Different End-point Energies6. Alpha Spectroscopy using Surface Barrier Detectors7. Beta and Conversion Electron Study

Recommended books :

1. Radiation Detection and Measurement G. F. Knoll, John Wiley (1988)2. Nuclear Electronics P. W. Nicholson, Wiley, London (1974)

PY521 Field Theory & Quantum Electrodynamics (4,0:4)

Lagrangian and Hamiltonian formulations, variational principle, Euler-Lagnrange equation, invariance of action and conservation laws, review of field quantization, quantization of guage field, invariance of electromagnetic field under Lorentz transformations, electromagnetic field in the Lorentz guage. Proca field.

Interaction of an electron field with the radiation field, discussion of guage invariance and minimal coupling – CPT theorem.

Covariant perturbation theory, S-matrix expansion in the interaction picture, Feynman diagrams and Feynman rules for Q.E.D. Thompson scattering, Compton scattering and Miller scattering. A brief introduction to charge and mass renormalization, Bethe’s treatment of Lamb shift.

Recommended books :1. Advance Quantum Mechanics J. Sakurai2. Relativistic Quantum Fields. Vols. I & II Bjorken and Drell3. Quantum Field Theory Mandl4. Particles and Fields Lurie5. Quantum Theory of Fields. Vols. I & II Weinberg

PY522 General Relativity and Gravitation (4,0:4)

Eotvos experiment, principles of equivalence and principle of general covariance.Tensor algebra and calculus, metric tensor, Christoffel symbols, geodesics covariant differentiation, parallel transport, curvature and scalar tensor.Einstein’s equation, Schwarchild solution, classic tests of general relativity.Cosmological principle, Robertson-Wallace metric Hubble constant.Physics of the early universe.

Recommended books :

1. Theory of Relativity P. G. Bergman2. Gravitation & Cosmology S. Weinberg3. General Relativity & Gravitation M. G. Bowler4. Introduction to General Relativity Narlikar

PY523 Particle Physics (4,0:4)

Introduction to Lie algebra of SU(2) and SU(3) multiplets, Gell Mann-Okubo mass formula, Quark and quarkonium states, justification for color.Relativistic kinematics, scattering cross section, life-times. Introduction to S-matrix, Feynmann diagrams, and matrix elements.Electromagnetic form factors, parton model and deep inelastic scattering.Historical development of weak interaction physics, V-A current-current interaction theory, Cabibbo theory, neutrino scattering neutral current, Vector Bosons, ideas about SSB and Salam-Weinberg model and its simple tests.

Recommended books :

1. Quarks & Leptons Halzen & Martin2. Introduction to Particle Physics Change & O’Neill3. Weak Interactions Commins & Bucksbaum

PY531 Superconductivity (4,0:4)

Phase transition in fluid and other systems with special emphasis on superconducting normal phase transition critical points, order parameters, critical exponents and equalities, Mean field theory, role of fluctuations, Ginzburg-Landau theory, fluctuations in Gaussian approximation, Scaling hypos thesis.

Basic properties of superconductors. Phenomenological thermodynamic treatment. Two fluid model; Magnetic behaviour of superconductors, intermediate state, London’s equations and penetration depth, quantized flux. Pippard’s non-local relation and coherence length. Ginzburg-Landau theory, variation of the order parameter and the energy gap with magnetic field, isotope effect; Energy gap and its measurement; magnetization, specific heat and thermal conductivity; electron-phonon interaction and cooper pairs, brief discussion of the B.C.S. theory, its results and experimental verification; (p- and d- wave pairs).

Tunneling in SIN and SIS sandwiches, practical details; Coherence of the electron-pair wave, Weak links; dc and ac Josephson effects, superconducting Quantum Interference Devices (SQUID).

Type II superconductivity, magnetization of type-II superconductors, mixed state, surface energy, specific heat, critical currents of type-II superconductors flux lattice, flux flow (creep).

Superconducting materials (only qualitative description) conventional low temperature superconductors, High temperature superconductors, heavy fermions system, boro-carbides.

Recommended books :

1. Introduction to Superconductivity M. Tinkham2. Superconductivity of Metals and Alloys P. G. deGennes3. Theory of Superconductivity J. R. Shrieffer

PY532 Magnetism (4,0:4)

Static Phenomena : Diamagnetism; Paramagnetism; Crystal-field effects; John-Teller effects; Adiabatic demagnetization; Molecular field theory of ferromagnetism; Heisenberg-exchange interaction; Superexchange; Ruderman-Kasuya and Yosida interaction; Series-expanison and Bethe-Peierls-Weiss methods; Spin Waves; Ginzburg-Landau theory of the ferromagnetism; Slater-Puling Curve; Shape, magnetocrystalline and other types of anisotropy; Micromagnetics; Origin and observation of ferromag- netic domins; Soft and hard magnetic materials; Different stages of magnetic ordering in alloys; Kondo, spin-glass, cluster spin-glass, inhomogeneous long-range characterization and the relevant theoretical concepts. Applications of bulk and thin film magnetic materials.

Dynamic Phenomena : Linear Response Theory : Magnetic response and relaxation; Generalized magnetic susceptibility; Kramers-Kronig relations; The fluctuation-Dissipation theorem.

Recommended books :

1. Physical Principles of Magnetism A. H. Morrish2. Physics of Magnetism S. Chikazumi3. Quantum Theory of Magnetism R. M. White4. Relaxation Phenomena in condensed matter S. Dattagupta

PY533 Semiconductor Physics (4,0:4)

Intrinsic and Extrinsic Semiconductors. Chemical binding in Semiconductors Typical Examples of Energy Band Calculations, Kinetic phenomena/transport properties, Diffusion of electrons and holes and recombination effectsCharacteristic Properties of Semiconductors and their determination.

Elemental Semiconductors (Ge, Si, Se and Te) and their properties, Important semiconductor compounds. Doping/Implantation in Semiconductors.

Defects in Solids: Grain and twin boundaries, Point Defects, line defects and planar defects or dislocations and their effects on solid state properties. Radiation damage in Solids and its effects on lattice and electronic properties, colour centres. Detection and study of defects by XRD, Electron Microscopy, and RBS/Channeling.

Introduction to Disorder: substitutional and structural disorder, short range and long range disorder.

Recommended books :

1. Introduction to Solid State Physics C. Kittel2. Semiconductors R. A. Smith3. Energy Bands in Semiconductors D. Long4. Solid State Electronics S. Wang

PY541 Elements of Nonlinear Optics (4,0:4)

Coherent interactions of radiation field with gaseous and solid state systems

Nonlinear optics : Introduction, second and third harmonic generation, third order nonliniarites, parametric amplification and oscillation, phase conjugate optics, anisotropic nonlinear media, dispersive media.

Guided wave optics : Planar dielectric wave guides, coupling of radiation to optical wave guides, distributed feedback lasers, electro-optic modulation and mode couplings in wave guides, fabrication of planar optical wave guides.

Optical fibers: step index and graded index fibers, attenuation, dispersion and propagation of light in fibers.

Nonlinear phenomena in guided wave geometry, Quasi phase matching, cascaded second order nonlinearity. Nonlinear optical fibres. Solitons in optical fibres.Recommended books :

1. Principles on Non-linear Optics Y. R. Shen2. Non-linear Optics N. Bloembergen3. Non-linear Optics R. W. Boyd4. Non-linear Optics Butcher & Cotter

PY542 Elements of Quantum Optics (4,0:4)

Quantum theory of Radiation – second quantization; Quantum statistical description of the radiation fields; Coherent states; Photon correlations; Squeezed states and applications; Theory of several process using second quantized formalism; spontaneous emission and stimulated emission; second order process, multiphoton absorption, and ionization with description of some experimental results.

Recommended books :

1. Introduction to Quantum Optics Baldwin2. Statistical Theory of Radiation Louisell3. Coherence & Quantum Optics Mandel & Wolf

PY543 Optical Resonance (4,0:4)

Resonant interaction of simple atomic systems with intense radiation field; Optical coherent transients such as free induction decay, optical nutation, photon echo, stimulated photon echo, and Ramsey fringes from separated fields; Area theorem, self induced transparency; Spontaneous emission and resonance fluorescence with excitation by intense radiation; Super radiance and cooperative phenomena; optical bistability, chaos in optical systems, spatial temporal patterns.

Recommended books :

1. Two Level Atom Allen & Eberly2. Lasers Eberly & Milloni3. Lasers & Quantum Optics Sargent & Meystre

Optional Courses

PY524 Lie Groups & Lie Algebra (4,0:4)

Continuous groups, Lie groups, examples like transition and rotation groups. Lorentz group, SU(2) 7 SU(3) groups. Statements of Lie’s theorem, Lie algebra, standard form of Lie algebra. Casimir invariants, roots and cartan classification of semi-simple Lie groups. Root diagrams for SU(2), SU(3) and SU(N). Dynkin diagrams.

Basic and irreducible representations of SU(2) & SU(N). Young tableau and its uses for Clebsch-Gordon decomposition. Classification of elementary particles in terms of representations of SU(3), SU(4) and SU(6), Dynamical symmetries, symmetry group of hydrogen atom.

Recommended books :

1. Classical Groups Wybourne2. Lie Groups & their Lie Algebra Gilmore3. Continuous Groups of Transformations Eisenhart

PY525 Dynamical Systems and Chaos (4,0:4)

Review of Hamiltonian dynamics: Special emphasis on the Hamiltonian-Jacobi theory and action-angle variable. Solutions of Hamilton’s equations etc., canonical transformations, phase space dynamics.

Integrable models: Definition of integrability for Hamiltonian systems, KAM theorem, classical perturbation theory.

Chaos in Hamiltonian systems and maps: Simple chaotic Hamiltonian systems, Lyapunov exponents, Poincare sections, power spectra, Kolmogorov entropy and other systems, noise analysis in electrical circuits, measures of chaos in Hamiltonian systems, simple maps, area preserving maps, fixed point and poincare Birkohoff theorems.

Dynamics of dissipative systems: Dissipative systems and turbulence, strange attractors, Lorentz and Rossler attractors.

Non-linear evolution equations and solitons: KDV equations, inverse scattering, application in particle and condensed matter physics.

Brief introduction to semi-classical and quantum chaos, examples from particle physics and condensed matter physics.

Numerical simulation of chaotic systems.

Text books :

Chaos and Integrability in Non-linear Dynamics by M. Tabor (Wiley)Regular and stochastic motion by Lichtenber & LiebermanChaos in Guage Theories by Biro Muller (World Scientific)

Algebric equation on vector spaces, Topological spaces, Differentiable manifolds, Tangent, cotangent spaces and tensors at a point, Vector fields, intrinsic differentiation processes on a differentiable manifold. Covariant differentiation, parallel transport and affine connection, Torsion and curvature, Differential forms, Homotopy and Cohomology, Applications to thermodynamics, Hamiltonian mechanics, guage theories, hydrodynamics, gravitation and cosmology.

Recommended books :

1. Geometrical Methods of Mathematical Physics B. Schutz2. Introduction to Topology, Differential Geometry and

Group Theory for Physicists S. Mukhi & N. Mukunda3. Symmetry Gauge Fields: Strings & Fundamental

Interactions. Vol. I Tulsi Dass4. General Relativity (Chapters @ & # and

Appendices A, B & C) R. M. Wald

PY534 Probes of Condensed Matter (4,0:4)

Investigation of structural and physical properties of solids using the following experimental techniques:

X-ray diffraction, neutron scattering, ion-beam channeling, electron microscopy, EPR/NMR/NQR, Mossbauer spectroscopy, positron annihilation, and other nuclear techniques.Thermal properties-specific heat thermal conductivity, thermal expansion, Differential Scanning Calorimetry Transport properties-ac and dc conductivity, Hall effect, magnetoresistanceMagnetic susceptibility, Magnetisation, HystresisRaman scattering and other optical probes

Recommended books :

1. X-ray Diffraction H. P. Klug and L. E. Alxander2. Methods of Experimental Physics Vol.21-Solid –

State Physics3. Nuclear Methods J. W. Mundy et. al. (Editors)4. Handbook of Microscopy, Applications in Materials Science.5. Solid State Physics and Chemistry S. Amelinckx et al. (Editors)6. Techniques of Metals Research R. F. Bunshah (Editor)7. Other books as prescribed by the instructor

PY535 Physics of Materials (4,0:4)

Chemical bonding in solids, Transition metal oxides: Structure of oxides and methods of structure determination, Perovskites, bronzes, ferrites and various oxide families, Metal – insulator transition. Superconducting materials, Ferroelectricity and related phenomena, Magnetism in oxides, Glasses and glass ceramics.

Metals and alloys: Phase diagrams of single component, binary and ternary systems, diffusion, nucleation and growth. Diffusional and diffusionless transformations. Mechanical properties. Metallic glasses. Preparation, structure and properties like electrical, magnetic, thermal and mechanical, applications.

Liquid Crystals: Mesomorphism of anisotropic systems, Different liquid crystalline phase and phase transitions, Few applications of liquid crystals.

Polymers: Physical properties and applications of polymers.

Recommended books :

1. Inorganic solids D. M. Adams (John-Wiley)2. Phase transformation in metal and alloys D. A. Porter and K. E. Easterling3. Fundamental of thermotropic liquid crystals deJen and Vertogen4. Electronic properties of polymers H. Kuzmany and S. Roth5. Metallic glasses K. Moorjani

PY536 Low Temperature Techniques (4,0:4)

Production of low temperatures; Principles of gas liquefaction & basic thermodynamics; Liquefaction cycles; Liquefaction and refrigerator systems; Philips liquid nitrogen and liquid helium plants, storage and transfer of liquid gases; Heat exchangers; Cooling with liquid helium; Dilution refrigerators; Adiabatic demagnetization; Nuclear demagnetization; Heat transfer; Temperature measurement and control; Thermal contact and isolation; Design of cryostats, vacuum techniques and materials for low temperature work. Devices based on superconducting properties.

Recommended books :

1. Experimental Techniques in Low Temperature Physics G. K. White2. Experimental Cryophysics F. E. Hoare et al.3. Cryogenic Systems R. Barren

PY537 Advanced Solid State Physics Laboratory (0,8:4)

1. Electrical resistivity of Ni in the temperature range 77K – 770K to separate out different scattering contributions to total resistivity and to study the magnetic phase transition.

2. Thermoelectric power in doped semiconductors down to 77K for the measurement of band gap and the type of carriers.

3. Hysteresis loops of soft and hard magnetic materials using electronic integrator method.

4. Ferromagnetic resonance measurements to determine magnetic anisotropy, spin re-orientation temperature and spin-wave excitations in magnetic systems.

5. Meissner and magnetic suspension lavitation effect and / or zero – resistance phenomenon in high temperature superconductors.

6. Determination of elastic constants of a cubic crystal by ultrasonic velocity measurements.

PY544 Ferroelectric and Electroceramics (4,0:4)

Nature of ceramics. Processing and Microstructural Characterization of ceramic materials. Linear and nonlinear dielectrics. Pyro-, piezo- and ferroelectricity in solids. Ferroelectrics as polar dielectrics. Theories of Ferroelectric phase transitions. Various families of ferroelectrics-Barium Titanate. Lead Titanate. KTP etc.

Domains in ferroelectrics and their experimental observation: Polarization switching mechanisms.

Applications to memories and displays, Non-switching applications including electro-optic, nonlinear-optic, piezoelectric, pyroelectric and elasto-optic applications. Emerging areas such as nanomaterials.

Solid State Ionic materials, Structure, Electrical and electro-chemical Properties and applications to fuel cells, batteries and chemical sensors.

Recommended books :

1. Introduction to Ceramics Kingrey2. Principles and Applications of Ferroelectric

and Related Materials Lines and Glass3. Ferroelectric Materials & their Applications Xu4. Superionic Solids-Principle and Applications S. Chandra

PY545 Liquid Crystals (4,0:4)

Mesomorphism in anisotropic fluids and amphiphilic systems: Nematic, cholestric and smectic (A, B, C and other exotic) phases of long rod like molecules; Nemataic and columnar phases of discotic molecules; Micelles; Hexagonal, cubic and lamellar phases of amphiphilic molecular systems.

Elastic continuum theory of liquid crystals; Defects and dynamics; Hydrodynamics and equilibrium theories.

Phase transitions and critical phenomena in liquid crystals; Phase diagrams of liquid crystalline mixures; Polar liquid crystals, frustration and re-entrant phenomena; Glassy states; Ferroelectric liquid crystals.

Liquid crystals in electric and magnetic fields; Electro-hydrodynamic instabilities; Kerr effect; Electro- optical effects; Twisted nematics and smectics.

Magnetic resonance and dielectric response in liquid crystals; Order parameters and molecular motions; Studies on oriented solutes.

Liquid crystal displays (active matrix, passive matrix and RMS responding displays) and optical communication devices; Application of liquid crystals in image and signal processing.

Recommended books :

1. The Physics of Liquid Crystals (2nd Edition) P. G. de Gennes and J. Prost2. Liquid Crystals (2nd Edition) S. Chandrasekhar3. Thermotropic Liquid Crystals-Fundamental G. Vertogen and W. H. de Jeu

PY546 Nonlinear Spectroscopic Techniques (4,0:4)

Brief introduction to tunable laser sources and linear spectroscopy; Physical principles underlying various spectroscopic techniques and line broadening phenomena; Resonant two and three level models for nonlinear response to intense laser radiation. Saturation spectroscopy, hole burning; coherent Raman spectroscopy, resonant four wave mixing for coherent anti-stokes Raman scattering; multiphoton ionization methods; life time measurements, Quantum beat spectroscopy, Hanle effect; Picosecond and femtosecond spectroscopic techniques for probing ultra fast dynamics, four wave mixing for determining dephasing times using intense incoherent light.

Recommended books :

1. Introduction to Nonlinear Spectroscopy M. D. Levenson2. Nonlinear Laser Spectroscopy V. S. Letokhov & V. P. Chebotayev3. Laser Induced Dynamic Gratings H. J. Eicher, P. Gunter & D. W. Pohl

PY547 Opto-electronics (4,0:4)

Basic Parameters of optical radiation, Radiometric, photometric and spectral parameters, coherence, polarization.

Luminiscence of semi-conductors, LEDs – parameters and characteristics of photodetectors, Photodiode types: PIN, Schottky barrier, heterojunction, phototransistor and photothyristor, photoresistors CCDs.

Optrons: Classification, input, transfer and isolation parameters, applications, reliability of optoelectronic devices.Optoelectronic devices for alphanumeric displays, optoelectronic devices for recording, transmission and image reproduction, picosecond optoelectronic devices, switching and sampling, fabrication of opto-electronic devices.

Electro-optics of anisotropic media, liquid crystals and photorefractive materials, electro-optic and acousto-optic modulations, electro-optic bean deflection.

Recommended books :

1. Semiconductor Optoelectronic Devices Pallab Bhattacharya2. Quantum Electronics Yariv3. Introduction to Optical Electronics K. A. Jones4. Optical Electronics A. K. Ghatak & K. Thyagarajan

PY548 Optical Cooling (4,0:4)

Brief survey of atomic spectra, including hyperfine interaction. Atomic ensemble, its interaction with resonant radiation, resonance fluorescence, energy momentum conservation, spontaneous emission line width, thermodynamic equilibrium. Optical pumping to new equilibrium state.Collision studies, microwave transitions, applications of optically pumped ensembles: Magnetometer, atomic clocks, weak interactions. Coupling of centre of mass motion with internal excitation by radiation and its use in cooling atoms, various cooling mechanisms: Doppler cooling, Optical molasses, Thermodynamic limit to lowest temperature, light shifts, gradient cooling – Sisphus cooling, optical pumping and cooling, coherent population trapping states, velocity selective coherent population trapping states. Ultra cold state, velocity distribution and quantum mechanical properties. Atomic maser and applications of cold beams.

Recommended books :

To be prescribed by the Instructor.

PY549 Cavity Quantum Electrodynamics (4,0:4)

Atoms in free space and in a generalized cavity. Weak and strong interactions regimes of cavity QED. Perturbative domain of cavity QED. Fermi Golden Rule, enhancement and inhibition of spontaneous emission, frequency shift. Atom near a mirror, atom in FP cavity. Atom-feild interaction in a high-Q cavity. Vacuum field Rabi splittings. Experimental results on enhancement/inhibition of spontaneous emission, vacuum Rabi splitting. Other cavity QED effects.Recommended books :

To be prescribed by the Instructor.

PY550 Coherence & Quantum Interference (4,0:4)

Coherence induced novel effects: Electromagnetic field induced transparency; ultra high refractive index, lasing without inversion, inversion without lasing, control of efficiency of nonlinear optical out put by extra resonant intense radiation, elimination of Kerr-nonlinear effects, correlated emission laser. Quantum interference, EPR arguments on quantum interference, Bell’s inequality, coincident detection, two photon interferrometry, experimental verification of Bell’s inequality, quantum non-demolition measurement, quantum transportation, quantum eraser, quantum computer.

Recommended books :

To be prescribed by the Instructure.PY538 Advanced Statistical Mechanics (4,0:4)

The Ising model: Multicomponent order parameters: The N-vector model: Exactly soluble models: Ising chain and a few other examples.

The reromalization group (RG) approach, Real-space and momentum-space RG methods and application to simple models.

Quantum fluids: BCS theory of superconductivity, liquid helium

Langevin and Fokker-Planck equations, Fluctuation-dissipation theorem. Linear response theory, non-equilibrium phase transitions.

Recommended books :

1. Equilibrium statistical physics M. Plischke and B. Bergesen2. Modern theory of critical phenomena S. K. Ma3. A modern course in statistical physics L. E. Reichl4. Statistical Mechanics J. K. Bhattacharya

PY539 Many Body Theory (4,0:4)

Systems of identical particles, Symmetric and anti-symmetric wave functions;

Interacting electron gas, Hartree and Hartree-Fock Approximations:

Second quantization for bosons and fermions, Time-dependent operators-Schrodinger, Heisenberg and interaction representations, Perturbative treatment of interacting electron gas problem, Random phase approximation.

Green function, Self energy, Dyson equation, Equation of motion method.Diagrammatic perturbation theory, Wick’s theorem, Feynman diagrams, applications to: electron gas, and many boson systems with condensed phase.

Recommended books :

1. Many Electron Theory S. Raimes2. Quantum Many-Particle Systems J. H. Negele & H. Orland3. Quantum Theory of Solids C. Kittel4. Many Particle Physics G. D. Mahan5. The Many-Body Problem W. E. Perry6. The Many-Body Problem D. Pines7. Green Functions in Solids E. N. Economou8. Interacting Fermi Systems Nozieres and Pines