university of gour banga department of physics
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University of Gour Banga
Department of Physics
Syllabus for the M. Sc. Course in Physics
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FOUR SEMESTER COURSE
TOTAL MARKS 1200
SEMESTER I (300 MARKS)
Four General Theoretical Papers:
Paper 101: Unit I - Mathematical Methods I (25 Marks)
Unit II - Classical Mechanics I (25 Marks)
Paper 102: Unit I - Quantum Mechanics I (25 Marks)
Unit II - Classical Electrodynamics I (25 Marks)
Paper 103: Unit I - Solid State Physics I (25 Marks)
Unit II - Electronics I (25 Marks)
Paper 104: Unit I - Atomic Spectroscopy (25 Marks)
Unit II - Experimental Methods in Physics (25 Marks)
Two General Practical Papers (100 Marks):
Paper 105: General Experiments (50 Marks)
(Practical Examination: 35 Marks + Internal assessment: 15 Marks)
Paper 106: Electronics Experiments (50 Marks)
(Practical Examination: 35 Marks + Internal assessment: 15 Marks)
SEMESTER II (300 MARKS)
Four General Theoretical Papers:
Paper 201: Unit I - Mathematical Methods II (25 Marks)
Unit II – Group Theory (25 Marks)
Paper 202: Unit I - Quantum Mechanics II (25 Marks)
Unit II - Classical Electrodynamics II (25 Marks)
Paper 203: Unit I – Statistical Mechanics I (25 Marks)
Unit II - Electronics II (25 Marks)
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Paper 204: Unit I – Classical Mechanics II (25 Marks)
Unit II - Nuclear Physics I (25 Marks)
Two General Practical Papers (100 Marks):
Paper 205: General Experiments (50 Marks)
(Practical Examination: 35 Marks + Internal assessment: 15 Marks)
Paper 206: Electronics Experiments (50 Marks)
(Practical Examination: 35 Marks + Internal assessment: 15 Marks)
SEMESTER III (300 MARKS)
Three General Theoretical Papers:
Paper 301: Unit I – Solid State Physics II (25 Marks)
Unit II – Nuclear Physics II (25 Marks)
Paper 302: Unit I – Molecular Spectroscopy (25 Marks)
Unit II – Computer Applications (25 Marks)
Paper 303: Introduction to Plasma Physics (50 Marks)
One Special Theoretical Paper:
Paper 304: Computational Physics I / (50 Marks)
Condensed Matter Physics I/
Advanced Electronics I
One General Practical Paper:
Paper 305: Computer Applications Practical (50 Marks)
One Special Practical Paper:
Paper 306: Special Practical I (50 Marks)
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SEMESTER IV (300 MARKS)
Three General Theoretical papers:
Paper 401: Unit I - Statistical Mechanics II (25 Marks)
Unit II – Astrophysics (25 Marks)
Paper 402: Unit I- Advanced Quantum Mechanics (25 Marks)
Unit II – Advanced Optics (25 Marks)
Paper 403: Unit I– Nonlinear Dynamics (25 Marks)
Unit II- Elective (25 Marks)
(Elements of General Relativity and Cosmology /
Liquid Crystal /
Plasma Waves and Instabilities)
One Special Theoretical Paper:
Paper 404: Computational Physics II / (50 Marks)
Condensed Matter Physics II/
Advanced Electronics II
One Special Practical Paper:
Paper 405: Special Practical II (50 Marks)
One Paper for project work:
Paper 406: Project (50 Marks)
SEMESTER I (300 Marks)
PAPER 101
Unit I: Mathematical Methods I [25 Marks]
1. Functions of a complex variable. Differentiability. Cauchy-Riemann equations. Harmonic functions.
Analytic functions. Entire functions. Multiple-valued functions. Branch points and branch cut. Riemann
surfaces. Complex integration. Contour integrals. Darboux inequality. Cauchy’s theorem. Cauchy’s integral
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formula. Liouville’s theorem. Morera’s theorem. Taylor and Laurent series. Singular points and their
classification. Residue theorem. Jordan’s lemma. Application of residue theorem to the evaluation of
definite integrals and the summation of infinite series. Integrals involving branch point singularity. Analytic
continuation. Schwarz reflection principle.
(13 L)
2. Linear vector spaces. Basis and dimension of a vector space. Inner product. Metric spaces. Cauchy-Scwartz
inequality. Linear independence and orthogonality of vectors, Gram-Schmidt orthogonalisation procedure.
Linear operators. Inverse of an operator. Dual spaces and adjoint operators. Special linear operators.
Projection operator. Matrix representation of linear operators. The algebra of matrices. Special matrices.
Rank of a matrix. Linear transformations. Change of basis. Eigenvalues and eigenvectors of matrices. The
Cayley-Hamilton theorem. Diagonalisation of matrices. Functions of matrices. Bilinear and quadratic
forms. Principal axis transformation. Solution of linear equations by matrix method.
(12 L)
Books Recommended:
(1) M. R. Spiegel: Theory and Problems of Complex Variables (Schaum’s outline
series).
(2) G. Arfken: Mathematical Methods for Physicists (Academic Press).
(3) J. Mathews and R. I. Walker :Mathematical Methods of Physics (Benjamin).
(4) P. Dennery and A. Krzywicki: Mathematics for Physicists (Harper and Row).
Unit II : Classical Mechanics I [25 Marks]
1. Review of Lagrangian and Hamiltonian formalisms. Legendre transforms. Hamilton’s function and
Hamilton’s equations of motion. Simple applications. Lagrangian and Hamiltonian of relativistic particles.
Principle of least action. Hamilton’s principle. Euler – Lagrange equations of motion from Hamilton’s
principle. Hamilton’s equations of motion from Hamilton’s principle. Noether’s theorem.
(8 L)
2. Canonical transformations. Examples. Integral invariants of Poincare. Lagrange and Poisson brackets as
canonical invariants. The equations of motion in Poisson bracket notation. Infinitesimal contact
transformation. Constants of the motion. Symmetry properties. Angular momentum Poisson bracket
relations. Liouville’s theorem. (8 L)
3. Hamilton-Jacobi equations for Hamilton’s principal and characteristic functions. The harmonic oscillator
problem by Hamilton-Jacobi method. Separation of variables in the Hamilton-Jacobi equation. Action-angle
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variables. The Kepler problem in action-angle variables. Passage from classical to quantum mechanics.
(9 L)
Books Recommended:
(2) H. Goldstein, C. Poole and J. Safko: Classical mechanics (Pearson).
(2) S. McCuskey: Introduction to advanced dynamics (Addison-Wesley).
(3) L. Landau and E. Liftshitz: Mechanics (Addison-Wesley).
(4) K.C. Gupta: Classical Mechanics ( New Age Books).
(5) N. Rana and P. Joag: Classical Mechanics (Tata McGraw-Hill).
(6) S. Sinha: Classical Mechanics (Narosa).
PAPER 102
Unit I: Quantum Mechanics I [25 Marks]
1. The wave equation of Schrödinger. The interpretation of the wavefunction. The superposition and
completeness of eigenstates. Expectation values of dynamic variables. Commutators and operator algebra.
Stationary states. The virial theorem. (3L)
2. Vector spaces in quantum mechanics. Hilbert space. Kets, bras and operators, Base kets and matrix
representation. Hermitian operator. Eigenkets as base kets. Orthogonality. Completeness. Postulates of
quantum mechanics. Observable and results of its measurement. The generalized uncertainty relation. Non-
commutating observables. Complete set of commuting observables. Change of basis. Unitary operators
Discrete and continuous bases. Coordinate and momentum representations. Linear harmonic oscillator by
operator method. Coherent states. (6 L)
3. Time-independent Schrödinger equation in one dimension. The free particle. The infinite square well. The
delta-function potential. The finite square well. Transmission coefficient. Schrödinger equation in three
dimensions. Schrödinger equation in spherical coordinates. The free particle as a central force problem.
Orbital angular momentum. Eigenvalue problem for Lz and L2. Spherical harmonics. The rigid rotator. The
spherical well with impenetrable walls. Spherical square well potential. Coulomb potential. The hydrogen
atom problem. Parity of wavefunctions. (7 L)
4. Approximation methods. Time-independent perturbation theory for non-degenerate and degenerate states.
Applications to anharmonic oscillator, Stark effect in hydrogen atom. Variational methods for ground and
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excited states. Application to the ground state of helium atom. (4 L)
5. Quantum Dynamics. Schrödinger, Heisenberg and interaction pictures. Evolution operator.
(3 L)
6. Identical particles. Symmetry under interchange. Wave functions for bosons and fermions. Slater
determinant. (2 L)
Books Recommended:
(1) E. Merzbacher: Quantum Mechanics (John Wiley and sons).
(2) D. Griffiths: Introduction to Quantum Mechanics (Pearson Education).
(3) A. K. Ghatak and S. Lokanathan: Quantum Mechanics (Macmillan India Ltd.).
(4) J. Sakurai: Modern Quantum Mechanics (Addison-Wesley).
(5) C. Cohen-Tannoudji et al : Quantum Mechanics Vol I and II (John Wiley).
(6) R. L. Liboff: Introductory Quantum Mechanics (Pearson Education).
(7) R. Robinett: Quantum Mechanics (Oxford University Press).
(8) M. Bellac: Quantum Physics (Cambridge University Press).
Unit II : Classical Electrodynamics I [25 Marks]
1. Review of electrostatics and magnetostatics: Formal solution of the electrostatic boundary value problem
with Green’s function; boundary value problems in Cartesian, spherical and cylindrical coordinates; Multiple
expansion; Electrostatics of macroscopic media. Magnetostatics. Simple boundary value problems.
(7 L)
2. Maxwell’s equations. Electromagnetic waves in nonconducting media. Energy and momentum of
electromagnetic waves. Propagation through linear media. Electromagnetic waves in conductors.
Monochromatic plane waves in conducting media. Free electrons in conductors and plasmas.
(5 L)
3. Radiation from accelerating electrical charges. The inhomogeneous wave equations. Retarded and advanced
potentials. Electric dipole radiation. Magnetic dipole radiation. Radiation from an arbitrary distribution of
charges and currents. Larmor formula. Radiation from a point charge. Lienard-Wiechert potentials. Fields of a
point charge in arbitrary motion. Power radiated by a point charge. Radiation from a charge undergoing linear
and circular motion. Bremsstrahlung. Cerenkov radiation. Relativistic electrodynamics. Covariant form of
electromagnetic equations. Transformation law for the electromagnetic field. Larmor precession.
(8 L)
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3. Radiation reaction force from energy conservation. Abraham - Lorentz evaluation of
the self-force. Difficulties with the Abraham-Lorentz model. The scattering and absorption of radiation by
bound charges. (5 L)
Books Recommended:
(1) J. Jackson: Classical Electrodynamics (Wiley Eastern).
(2) J. Marion: Classical Electromagnetic Radiation (Academic Press).
(3) W. Panofsky and M. Phillips: Classical Electricity and Magnetism (Addison-
Wesley).
(4) D. Griffith: Electrodynamics (Prentice Hall India).
PAPER – 103
Unit I: Solid State Physics I [25 Marks]
1. Crystalline and amorphous solids. The crystal lattice. Basis vectors. Unit cell. Symmetry operations. Point
groups and space groups. Plane lattices and their symmetries. Three dimensional crystal systems. Miller
indices. Directions and planes in crystals. Inter-planar spacings. Simple crystal structures: FCC, BCC, NaCl,
CsCl, diamond and ZnS structures, HCP structure. (5L)
2. X-ray diffraction by crystals. Laue theory. Interpretation of Laue equations. Bragg’s law. Reciprocal lattice.
Ewald construction. Atomic scattering factor. Experimental methods of x-ray diffraction. Comparative study
of X-ray, neutron and electron diffraction. (4 L)
3. Types of bonding. The van der Waals bond. Cohesive energy of inert gas solids. Ionic bond. Cohesive
energy and bulk modulus of ionic crystals. Madelung constant. The covalent bond. Metallic bond.
(4 L)
4. Vibrations of one-dimensional monatomic and diatomic lattices. Infrared absorption in ionic crystals (one-
dimensional model). Normal modes of harmonically vibrating solids. Phonons. Frequency distribution
function. Debye’s theory of lattice specific heat. Anharmonic effects. Thermal conductivity of insulators.
(5 L)
5. Quantized free electron theory. Fermi energy, wave vector, velocity and temperature. Density of states in
one, two and three dimensions. Electronic specific heat. Pauli spin paramagnetism. Free electron theory of
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electrical and thermal conductivity. AC conductivity and optical properties. Plasma oscillations. Hall effect.
Hall coefficient in one- and two- band models. (7 L)
Books recommended:
(1) F.C.Phillips: An introduction to crystallography (Wiley).
(2) C. Kittel: Introduction to Solid State Physics (Wiley Eastern).
(3) J. Christmaan: FundamentaL of Solid State Physics (John Wiley and Sons).
(4) M. Ali Omar: Elementary Solid State Physics (Pearson Education).
Unit II : Electronics I [25 Marks]
1. Passive Networks. Synthesis of two terminal reactive networks. Driving point impedance and admittance,
Foster’s reactance theorems. Canonic networks. (2 L)
2. Four-terminal two-port network. Parameters for symmetrical and asymmetrical networks. Image, iterative and
characteristic impedances. Propagation function. Lattice network. Bisection theorem and its application.
(2 L)
3. L-C filters. LPF, HPF, BPF and BRF type constant-k prototype filters. m-derived filters (principle only).
Attenuators. T-type, Pi-type, Bridged-T type lattice attenuators. (4 L)
4. High Frequency transmission line. Distributed parameters. Primary and secondary line constants; Telegraphers’
equation. Reflection co-efficient and VSWR. Input impedance of loss-less line. Distortion of em wave in a
practical line. (4 L)
5. Semiconductor Devices:
(a) p-n junction physics. Fabrication steps. Thermal equilibrium condition. Depletion capacitance. Current-voltage
characteristics. Charge storage and transient behaviour. Junction breakdown. Heterojunction.
(b) Characteristics of some semiconductor devices: BJT, JFET, MOS, LED, Solar cell,Tunnel diode, Gunn diode
and IMPATT. (8 L)
6. Active Circuits. Transistor amplifiers. Basic design consideration. High frequency effects. Video and pulse
amplifier. Tuned amplifier. Feedback in amplifiers. Harmonic self-oscillators. Steady state operation of self-
oscillator. Nonlinear equation of self-oscillator. (5 L)
Books Recommended:
(1) J. Ryder: Networks Line and Fields (PHI).
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(2) Frazier: Telecommunications.
(3) Zee: Physics of Semiconductor Devices (Wiley).
(4) Milman and Grable: Microelectronics(Tata McGraw-Hill).
(5) Chattopadhyay and Rakshit:, Electronic Circuit Analysis (New Age International).
PAPER –104
Unit I: Atomic Spectroscopy [25 Marks]
1. Spectra of hydrogenic atoms. Spectra of alkali atoms. Quantum defect. Penetrating and non-penetrating
orbits. Introduction to electron spin. Spin-orbit interaction and fine structure. Relativistic correction to spectra
of hydrogen atom. Lamb shift. The Lande g factor. Zeeman and Paschen-Back effects.
(9 L)
2. Spectra of divalent atoms. Singlet and triplet states of divalent atoms. L-S and j-j coupling. Magnetic field
effects. Spectra of Many-electron atoms. Pauli exclusion principle. Periodic classification of elements.
Equivalent and non-equivalent electrons. Terms of equivalent electrons.
(9 L)
3. Hyperfine structure in spectra of monovalent atoms. Origin of X-ray spectra. Screening constants. Fine
structure of X-ray leveL. Spin-relativity and screening doublet laws. Non-diagram lines. Auger effect.
(4 L)
4. Broadening of spectral lines. Natural width of spectral lines, Doppler broadening.
(3 L)
Books Recommended:
(1) H. White: Introduction to Atomic Spectra (McGraw-Hill).
(2) B. Bransden and C. Joachain: Physics of Atoms and Molecules (Longman).
(3) S. Ghoshal: Atomic and Nuclear Physics Vol I (S. Chand).
(4) V. Jain: Introduction to Atomic and Molecular Spectroscopy (Narosa).
(5) M. Weissbluth: Atoms and Molecules (Academic Press).
Unit II Experimental Methods in Physics [25 Marks]
1. Data interpretation and analysis, Precision and accuracy. Error analysis, propagation of errors, Least square
fitting, curve fitting. (4 L)
2.Transducers (pressure/vacuum, temperature, magnetic field, vibration particle detector, optical)
measurement and control. (8 L)
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3. Analog and digital Signal processing. Measurement with C.R.O. (5 L)
4. Experiments with interferometers and spectrometers (4 L)
5. Measurement of resistance (low and high), capacitance and inductance. Measurement of film thickness,
Refractive index of a dielectric media.
(4 L)
General Practical Papers:
Paper 105: General Experiments (List of Experiments provided) [50 Marks]
Paper 106: Electronics Experiments (List of Experiments provided) [50 Marks]
SEMESTER II (300 MARKS)
PAPER 201
Unit I: Mathematical Methods II [25 Marks]
1. Fourier and Laplace transforms. Inverse transforms. Covolution theorem. Solution of ordinary and partial
differential equations by transform methods. (8 L)
2. Green’s functions for ordinary and partial differential equations of mathematical physics. Integral
equations. Fredholm and Volterra equations of the first and second kinds. Fredholm’s theory for non-
singular kernel. (8 L)
3. Tensor analysis. Coordinate transformations. Scalars. Covariant and contravariant tensors. Outer product.
Inner product. Contraction. Symmetric and antisymmetric tensors. Quotient law. Metric tensor. Conjugate
tensor. Length and angle between vectors. Associated tensors. Raising and lowering of indices. The
Christoffel symbols and their transformation laws. Covariant derivative of tensors.
(9 L)
Books Recommended:
(1) L. Andrews and B. Shivamoggi,: Integral Transforms for Engineers (PHI).
(2) A. Joshi: Matrices and Tensors (Wiley Esstern).
(3) G. Arfken: Mathematical Methods for Physicists (Academic Press).
Unit II: Group Theory [25 Marks]
1. Groups. Definition and examples. Order of a group. Multiplication table. Rearrangement theorem.
Generators of a finite group. Conjugate elements and classes. Subgroups. Cayley’s theorem. Cosets.
Lagrange’s theorem. Direct product of groups. Invariant subgroups. Factor group. Isomorphism and
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homomorphism. Permutation groups. Distinct groups of a given order. Cyclic and noncyclic groups.
(7 L)
2. Group representations. Definition of representation. Faithful and unfaithful representations. Equivalent
representations. Invariant subspaces and reducible representations. Reducibility of a representation.
Irreducible representation. Schur’s lemmas. Great orthogonality theorem and its geometrical interpretation.
Characters of a representation. First and second orthogonality theorems of characters. Regular representation.
Projection operators. Direct product groups and their representations. Construction of character tables of
simple groups. (8 L)
3. Discrete, continuous, and mixed continuous groups. Topological and Lie groups. Axial rotation group
SO(2). Rotation group SO(3). Special unitary groups SU(2), SU(3) and their applications in physics.
(5 L)
4. Group of the Schrödinger equation. Symmetry and degeneracy. Good quantum numbers. Reduction due to
symmetry. Perturbation and level splitting. Matrix element theorem. Selection rules for electric dipole
transitions. (5 L)
Books Recommended:
(1) M. Tinkham: Group Theory and Quantum Mechanics (McGraw-Hill).
(2) A. Joshi: Group Theory (Wiley Eastern).
(3) F. Cotton: Chemical Applications of Group Theory (Wiley Eastern).
(4) T. Dass and S. Sharma: Mathematical Methods in Classical and Quantum Physics
(Universities Press).
(5) W. Tung: Group Theory in Physics (World Scientific).
PAPER 202
Unit I: Quantum Mechanics II [25 Marks]
1. Generalised angular momentum. Infinitesimal rotation. Generator of rotation. Commutation rules. Matrix
representation of angular momentum operators. Spin. Pauli spin matrices. Eigenspinors. Electron in static
magnetic field. Larmor precession. Electron in an oscillating magnetic field. Addition of two angular
momenta. Simple examples. Clebsch-Gordan co-efficients. Recursion relations.
(8 L)
2. Discrete and continuous space-time symmetries. Invariance principles and conservation laws. Space
translation. Time translation. Space rotation. Irreducible spherical tensor operators. Wigner-Eckert theorem.
Space inversion. Time reversal. Kramers degeneracy. (5 L)
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3. Time-dependent perturbation theory. Constant and harmonic perturbations. Perturbation coupling two
discrete states. Fermi’s golden rule. Sudden and adiabatic approximations. Interaction of an atom with
electromagnetic wave. Electric dipole radiation. (6L)
4. Scattering theory. Scattering amplitude. Differential and total cross sections. Integral equation for potential
scattering. Green’s function. Born approximation and its validity. Yukawa potential. Rutherford scattering
formula. Method of partial waves. Phase shifts. Optical theorem. Scattering by a hard sphere.
(6 L)
Books Recommended:
(1) E. Merzbacher: Quantum Mechanics (John Wiley and sons).
(2) D. Griffiths: Introduction to Quantum Mechanics (Pearson Education).
(3) A. K. Ghatak and S. Lokanathan: Quantum Mechanics (Macmillan India Ltd.).
(4) J. Sakurai: Modern Quantum Mechanics (Addison-Wesley).
(5) C. Cohen-Tannoudji et al : Quantum Mechanics VoL I and II (John Wiley).
(6) R. L. Liboff: Introductory Quantum Mechanics (Pearson Education).
Unit II: Classical Electrodynamics II [25 Marks]
1. Relativistic Electrodynamics: Tensors in minkowski space, Electromagnetic field tensor, Covariance of
electrodynamics, Transformation of electromagnetic field. Relativistic Lagrangian and Hamiltonian and
Hamiltonian of a charged particle in an electromagnetic field. Lagrangian for electromagnetic field; stress
tensors, conservation laws (10L)
2. Scattering from a free electron. Thomson scattering. Scattering from a bound electron. Rayleigh scattering.
Absorption of radiation by a bound electron. Normal and anomalous dispersion. Lorentz’s electromagnetic
theory. Causality and dispersion relations. Kramers-Kronig relations. (8 L)
3. Propagation of electromagnetic waves through dielectric and metallic media. Effect of external magnetic
field on wave propagations. Ordinary and extraordinary rays. Wave guides
(7 L)
Books Recommended:
(1) J. Jackson: Classical Electrodynamics (Wiley Eastern).
(2) J. Marion: Classical Electromagnetic Radiation (Academic Press).
(3) S. Puri: Classical Electrodynamics (Tata McGraw-Hill).
(4) D. Griffith: Electrodynamics (Prentice Hall India).
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(5) Chen- Plasma Physics
PAPER 203
Unit I: Statistical Mechanics I [25 Marks]
1. Scope and aim of statistical mechanics. Transition from thermodynamics to statistical mechanics. Review
of the ideas of phase space, phase points, and ensemble. Density of phase points. Liouville’s equation and
Liouville’s theorem. (3 L)
2. Stationary ensembles: Micro canonical, canonical and grand canonical ensembles. Partition function
formulation. Fluctuation in energy and particle. Equilibrium properties of ideal systems: ideal gas, Harmonic
oscillators, rigid rotators. Para magnetism, concept of negative temperature. (10 L)
3. Density matrix: Idea of quantum mechanical ensemble. Statistical and quantum mechanical approaches.
Pure and mixed states. Density matrix for stationary ensembles. Application to a free particle in a box, and an
electron in a magnetic field. Density matrix for a beam of spin 1/2 particles. Construction of the density
matrix for different states (pure and mixture) and calculation of the polarization vector.
(8 L)
4. Distribution functions. Bose-Einstein and Fermi-Dirac statistics. General equations of state for ideal
quantum systems. (4 L)
Books Recommended:
(1) R. Pathria: Statistical Mechanics
(2) K. Huang: Introduction to Statistical Mechanics
(3) S. Salinas: Introduction to Statistical Mechanics.
(4) F. Reif: FundamentaL of Statistical and Thermal Physics.
(5) R. Kubo: Statistical Mechanics.
Unit II: Electronics II [25 Marks]
1. Op-Amp Circuits. Characteristics of ideal and practical op-amp. Nonlinear amplifiers using op-amps. Log
amplifier, anti-log amplifier, regenerative comparators. Active filters. Precision rectifiers. ADC and DAC
circuits. Op-amp based self-oscillator circuits. RC phase shift, Wien bridge, Non-sinusoidal oscillators.
(7 L)
2. Voltage Regulators. Series op-amp, IC, Switching regulators. (2 L)
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3. Elements of communication electronics. Principles of analog modulation- linear and exponential types.
Comparison among different techniques- power, bandwidth and noise immunity consideration. Generation of
transmitted carrier and suppressed carrier type AM signals. Principles of FM and PM signal generation.
Principles of detection of different types of modulated signals (TC and SC types). Modulation techniques in
some practical communication systems. AM and FM radio. VSB AM and QAM techniques in TV
broadcasting. (10 L)
4. Digital circuits. Logic functions. Logic simplification using Karnaugh maps. SOP and POS design of logic
circuits. MUX as universal building block. RS, JK and MS-JK flip-flops. Registers and counters (principle
only). (6 L)
Books Recommended:
(1) R. Jain: Modern Digital Electronics (Tata McGraw-Hill).
(2) J. Ryder: Electronics FundamentaL and Application (PHI).
(3) Gaykwad: Operational Amplifier.
(4) Roddy and Coolen: Electronic Communication Systems (PHI).
PAPER 204
Unit I: Clasical Mechanics II [25 marks]
1. Special Theory of Relativity: Lorentz transformation; 4-vector(time space and light like), 4-velocity and
acceleration; 4-momentum and force. Relativistic invariants and kinematics: Decay, elastic collision and
reaction, Lagrangian and Hamiltonian of relativistic particle. ( 10L)
2. Rigid body motion. Euler’s equations of motion. Force-free motion of a rigid body. Heavy symmetrical top
with one point fixed. Fast and sleeping top. (4 L)
3. Continuous system anf fields: Clasical Lagrangian and Hamiltonian density, equation of motion,
conservation theorems. (3L)
4. Deformable bodies. Strain and stress tensors. Energy of elastic deformation. Hooke’s law and stiffness
constants. (2 L)
5. Fluid dynamics: Motion of a perfect fluid: Equation of continuity. Euler’s and Bernoulli’s equation of
motion for a perfect fluid. Kelvin’s theorem on circulation. Helmholtz’s vorticity theorem. Flow of imperfect
fluids. Navier-Stokes’ equation. (6 L)
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Books Recommended:
(2) H. Goldstein, C. Poole and J. Safko: Classical mechanics (Pearson).
(2) S. McCuskey: Introduction to advanced dynamics (Addison-Wesley).
(3) L. Landau and E. Liftshitz: Mechanics (Addison-Wesley).
(4) K.C. Gupta: Classical Mechanics ( New Age Books).
(5) N. Rana and P. Joag: Classical Mechanics (Tata McGraw-Hill).
(6) S. Sinha: Classical Mechanics (Narosa).
Unit II: Nuclear Physics I [25 Marks]
1. General properties of nuclei. Nuclear radius and charge distribution. Charge radius of nucleus from electron
scattering experiment and the study of muonic x-rays. Charge form factor. Nuclear binding energy. Semi-
empirical mass formulas. Angular momentum and parity of nuclei. Magnetic dipole moment. Electric
quadrupole moment and nuclear shape. (6 L)
2. Two-nucleon problem and nuclear forces. Ground and excited states of deuteron. Two-nucleon scattering.
n-p scattering. Partial wave analysis. Phase-shift. Scattering length. Low energy p-p scattering (qualitative
discussion). Charge symmetry and charge independence of nuclear forces. Isospin symmetry. Exchange
interaction. Elementary discussion on Yukawa’s theory. (6 L)
3. Nuclear modeL. Fermi gas model. Extreme single particle models. Spherical shell model. Collective model.
Nilsson model. (4 L)
4. Nuclear reactions. Conservation laws. Energetics. Q-value. Spontaneous fission. Mass and energy
distribution of fragments. Direct and compound nuclear-reactions. Experimental verification of Bohr’s
independence hypothesis. Resonance reactions. Breit-Wigner dispersion relation. Stripping and pick up
reactions (qualitative discussion only). Optical model. (5 L)
5. Particle accelerators. Pelletron. Tandem principle. Synchrotron and synchrocyclotron. Colliding beams.
Threshold energy for particle production. (4 L)
Books Recommended:
(1) S. Ghoshal: Atomic and Nuclear Physics Vol II (S. Chand).
(2) S. Wong: Introductory Nuclear Physics (PHI).
(3) I. Kaplan: Nuclear Physics (Narosa).
(4) K. Heyde: Basic Ideas and Concepts in Nuclear Physics (Institute of Physics Publishing).
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(5) B. Cohen: Concepts of Nuclear Physics (McGraw-Hill, India).
General Practical Papers:
Paper 205: General Experiments (List of Experiments provided) [50 Marks]
Paper 206: Electronics Experiments (List of Experiments provided) [50 Marks]
SEMESTER III (Total 300 Marks)
PAPER 301
Unit I: Solid State Physics II [25 Marks]
1. Magnetic properties of solids. Diamagnetism, Langevin equation. Quantum theory of paramagnetism.
Curie law. Hund's rules. Paramagnetism in rare-earth and iron-group ions. Elementary idea of crystal field
effects. Ferromagnetism. Curie-Weiss law. Heisenberg exchange interaction. Mean field theory.
Antiferromagnetism. Neél point. Other kinds of magnetic order. Nuclear magnetic resonance.
(6 L)
2. Quantized free electron theory. Fermi energy, wave vector, velocity and temperature. Density of states in
one, two and three dimensions. Electronic specific heat. Pauli spin paramagnetism. Free electron theory of
electrical and thermal conductivity. AC conductivity and optical properties. Plasma oscillations. Hall effect.
Hall coefficient in one- and two- band models. (6 L)
3. Intrinsic and extrinsic semiconductors. Carrier concentration. Fermi levels of intrinsic and extrinsic semi-
conductors. Bandgap. Direct and indirect gap semiconductors. Hydrogenic model of impurity levels.
(2 L)
4. Energy bands in solids. The Bloch theorem. Bloch functions. Review of the Kronig-Penney model.
Brillouin zones. Number of states in the band. Band gap in the nearly free electron model. The tight binding
model. Electron dynamics in an electric field. The effective mass. Concept of hole.
(5 L)
4. Superconductivity, Survey of important experimental results. Critical temperature. Meissner effect. Type I
and type II superconductors. Thermodynamics of superconducting transition. London equations. London
penetration depth. Energy gap. Basic ideas of BCS theory. High-Tc superconductors.
(4 L)
5. Optical Properties of Solids (2 L)
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Books recommended:
(1) N. Ashcroft and N. Mermin: Solid State Physics (Holt, Reinhart and Winston).
(2) M. Ali Omar: Elementary Solid State Physics (Pearson Education).
(3) C. Kittel: Solid State Physics (Wiley Eastern).
Unit II: Nuclear Physics II [25 Marks]
1. Beta and Gamma decay. Fermi’s theory of beta decay. Allowed and forbidden transitions. Selection rules.
Non-conservation of parity in beta decay. Detection of neutrino. Gamma–decay and selection rules
(derivation of transition probabilities not required). Internal conversion. (5 L)
2. Energy loss of charged particles and gamma rays. Ionization formula, Stopping power and range. Radiation
detectors. Multiwire proportional counter. Scintillation counter. Cerenkov detector. (5 L)
3. Reactor Physics. Slowing down of neutrons in a moderator. Average log decrement of energy per
collision. Slowing down power. Moderating ratio. Slowing down density. Fermi age equations. Four-factor
formula. Typical nuclear reactors. (5 L)
4. High energy physics. Types of interaction in nature. Typical strengths and time-scales. Conservation laws.
Charge-conjugation. Parity and Time reversal. CPT theorem, Gell-Mann-Nishijima formula. Intrinsic parity
of pions. Resonances. Symmetry classification of elementary particles. Quark hypothesis. Charm, beauty and
truth. Gluons. Quark-confinement. Asymptotic freedom.
(10 L)
Books Recommended:
(1) R. Roy and B. Nigam: Nuclear Physics (Wiley Eastern).
(2) W. Meyerhoff: Elements of Nuclear Physics (McGraw-Hill).
(3) W. Burcham and M. Jobes: Nuclear and Particle Physics (Addison-Wesley).
(4) A. Das and T. Ferbel: Introduction to Nuclear and Particle Physicss (World Scientific).
(5) D. Perkins: Introduction to High Energy Physics (Addison-Wesley).
PAPER 302
Unit I: Molecular Spectroscopy [25 marks)]
1. Born-Oppenheimer approximation and separation of electronic and nuclear motions in molecules. Band
structure of molecular spectra. Hydrogen molecule ion. Molecular orbitals. Hydrogen molecule. Valence band
18
approach. Coulomb and exchange integrals. Electronic structure of simple molecules. Chemical bonding.
Hybridization. (5 L)
2. Microwave and far infrared spectroscopy. Energy levels of diatomic molecules from rigid and non-rigid
rotator models. Selection rules. Structure determination. Isotope effect. Rotational spectra of polyatomic
molecules. (5 L)
3. Infrared Spectra. Harmonic and anharmonic (no deduction) models for vibrational energy levels of
diatomic molecules. Selection rules. Morse potential. Energy curves. Dissociation energy. Isotope effect.
Rotational-vibrational coupling. Symmetry of molecular wavefunctions and nuclear spin. (5 L)
4. Raman spectroscopy. Rotational, vibrational, Rotational-vibrational Raman spectra. Stokes and anti-Stokes
Raman lines. Selection rules. Nuclear spin and its effect on Raman spectra.
(3 L)
5. Vibrational spectra of polyatomic molecules. Normal modes. Selection rules for Raman and infrared
spectra. Normal modes of CO2 and other simple triatomic molecules. (3 L)
6. Electronic spectra of diatomic molecules. Vibrational band structure. Progressions and sequences. Isotope
shift. Intensity distribution in vibrational structure of electronic spectra. Franck-Condon principle. Rotational
structure of electronic spectra. P-, Q-, and R- branches. Band head formation.
(4 L)
Books Recommended:
1. G. Herzberg: Molecular Spectroscopy (Diatomic Molecules) (Van Nostrand).
2. G. Barrow: Molecular Spectroscopy (McGraw-Hill).
3. J. Hollas: Modern Spectroscopy (John-Wiley and Sons).
4. C. Banwell and E. McCash: Fundamentals of Molecular Spectroscopy (TMH).
5. G. Aruldhas: Molecular Spectroscopy
Unit II: Computer Applications [25 Marks]
1. Elements of C Programming Language: Algorithms and flowchart. Structure of a high level language
program. Features of C language. Constants and variables. Expressions. Input and output statements.
Conditional statements and loop statements. Arrays. Functions. Character strings. Structures. Pointer data
type. List and trees. (9L)
2. Numerical techniques: Approximate numbers and Significant digits, Types of errors, General formula for
errors, Order of errors. (3 L)
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3. Representation of integers and real numbers. Accuracy. Range. Overflow and underflow of number
representation. Error propagation and instability. Solution of polynomial equations- bisection and Newton-
Raphson algorithms. Solution of a system of simultaneous equations- Gauss elimination, Gauss-Seidel, LU
decomposition algorithms. Interpolation- Newton’s interpolation formulae. Numerical integration –
trapezoidal formula, Simpson’s formula, Romberg formula. Numerical solution of differential equations-
Euler and Runge-Kutta formulae. Numerical solution of partial differential equations- discussion of
algorithms only. Monte Carlo technique of numerical integration.
(13 L)
Books Recommended:
(1) Tanenbaum, Operating system (Prentice Hall).
(2) Gottfried, Programming with C (Schaum series).
(3) Balaguruswamy, ANSI C. (Tata McGraw-Hill).
PAPER 303 [50 marks]
Introduction to Plasma Physics
1. Elementary concepts of Plasma, Occurrence of plasma in nature, Concept of temperature, Concept of
Debye shielding, Plasma sheath, Plasma oscillation, plasma parameters, plasma criteria, Applications of
plasma physics. (8 L)
2. Motion' of charged particles in electromagnetic field: Uniform E and B fields, non- uniform fields :
special variations of magnetic fields, gradient drift, parallel acceleration of guiding center, magnetic mirror
effect, time-varying E and B fields: slowly time varying E fields, time varying B fields and space varying E-
fields Adiabatic invariants: first, second and third adiabatic invariants. (10 L)
3. Hydrodynamical description of plasma: Fundamental fluid equations of Plasma, Fluid drift perpendicular to
B, Fluid drift parallel to B, the plasma approximation. (6L)
4. Waves modes in Plasma: Electron plasma waves, sound waves, Ion waves, Comparison of ion and
electron wave. Electrostatic wave perpendicular to B and parallel to B , Electrostatic ion cyclotron wave,
Electromagnetic wave perpendicular to B and parallel to B. Alfven wave.
(10 L)
5. Hydromagnetic equilibrium, concept of β. Diffusion of magnetic fields in plasma, plasma instabilities:
Gravitational Two stream, Weibel instability (5 L)
20
6. Diffusion and mobility in weakly ionized plasmas. Collision parameters, Ambipolar diffusion coefficient,
Recombination. Plasma resistivity (5L)
7. Plasma kinetic theory: equation of kinetic theory, derivation of fluid equations, plasma oscillations and
Landau damping (qualitative discussion) and resonant particle. Experimental verification of Landau damping
(6 L)
PAPER 304: [Special Paper-A/B/C]
A. Advanced Electronics I [50 marks]
1. IC Technology: Hybrid and monolithic IC. Semiconductor processing: Diffusion, implantation, Oxidation,
Epitaxy, lithography. Si IC technology: MOS and Bipolar. Packaging and testing.
(5 L)
2. Analog Integrated Circuits. Differential amplifier, OP-AMP comparator. Continuous time filters. Switched
capacitance implementation of sample data filters. Analog multiplexers. PLL and frequency synthesizer.
(10 L)
3. Digital Integrated Circuits: Logic families – TTL, ECL, MOS, MESFET. Design of combinational and
sequential circuits – MUX, decoder/ encoder, registers, counters, gate arrays. Programmable logic devices –
PAL, GAL, PLA. Programmable gate arrays. (8 L)
4. Special purpose ICs. ICs for analog communication. Digital signal processing ICs. Basic concepts of MIC,
MMIC and OELC. GaAs technology; (5 L)
5. Memories: Sequential and Random access memories. RAM bipolar and MOS static and dynamic
memories. Programmable memories: PROM, EPROM, EEPROM. (7L)
6. Microprocessors and their applications. Architecture of 8 bit (8085) and 16 bit (8086) microprocessors.
Addressing modes and assembly language programming of 8085 and 8086. Machine cycles and their timing
diagrams. Interfacing concepts. Memory and I/O interfacing. Interrupts and interrupt controllers.
Microprocessor based system design. Comparison of different microprocessors.
(15 L)
Books Recommended:
(1) Geiger, Allen and Strader: VLI – Design Techniques for Analog and Digital
Circuits.
21
(2) Gray and Meyer: Analysis and Design of Analog Integrated Circuits.
(3) A Mathur: Microprocessors.
(4) R. Gaonkar: Microprocessor Architecture, Programming and Applications with
8085/8085A (Second Edition Penram International Publishing, India).
(5) Lin and Gibson : Microprocessor (PHI).
(6) S Soelof : Applications of Analog Integrated Circuits (PHI).
(7) B. Brey: Intel Microprocessors Architecture, Programming and Interfacing (PHI).
B. Computational Physics I [50 marks]
1. Fundamentals of Language and Numerical methods (15 L)
2. Classical Mechanics and: Numerical simulation of central field orbits; Application of classical perturbation
theory. (15 L)
3. Non-linear Dynamics: Phase plot and phase trajectories; Bifurcations- saddle node, pitch fork, transcritical
Hopf bifurcations; Lorenz equation and study of chaos; Vander pol, Chua and other systems.
(20 L)
C. Condensed Matter Physics I [50 Marks]
I. Fundamentals of Many Electron Systems : Hartee Fock Theory: The Basic Hamiltonian in a Solid –
Electronic and Ionic Parts. The Adiabatic Approximation. Single Particle Approximation of the Many
Electron System: Single Product and Determinantal Wave Functions, Matrix Elements of one and two particle
Operators. The Hatree Fock
(HF) Theory. The HF Equation. Exchange Interaction and Exchange Hole, Koopmans Theorem. The
occupation Number Representation – The Many Electrons Hamiltonian in Occupation Number
Representation. The HF Ground State Energy. (12L)
II. The Interacting Free Electron Gas : Quasi Electrons and Plasmon: The HF Approximation of the Free
Electron Gas. Single Particle Energy Levels, the Ground state energy. Calculation of the Ground State
Energy. Cohesive Energy in Metals. Screening and Plasmons. Experimental Observations of Plasmons. The
Dielectric Function of the Electron Gas. Friedel Oscillations. Landau’s QuasiParticle Theory of Fermi Liquid.
Strongly Colelated Electron Gas. Mott Transition.
(12L)
22
II. Coherence and Correlation: Types of Coherence. Density Matrix Formalism. Quantum Coherent Effects.
Correlation Functions and Noise. Particle Particle Correlation. The Fluctuation – Dissipation Theorem.
Current Fluctuations and the Nyquist Formula. The Kubo Formula and ManyBody Theory of Metals.
Messoscopic Effects. (8L)
IV. Spin and Magnetic System:
Overview of Magnetic Properties. The Ising Model: Zero External Magnetic Field; Spontaneous Symmetry
Breaking, External Magnetic FieldHysteresis. Critical Fluctuations: Other magnetic models, Multicritical
behaviour, Metamagnets, Critical Exponents and Magnetic Susceptibility, Landau Coarse Graining Theory.
renormalization Group Methods, Spin Waves and Goldstone Bosons. SpinSpin Interactions: Ferromagnetic
Instability, Localized States and RKKY Exchange Interactions. Spin Flip and Spin Dephasing.
(10L)
V. Superconductivity Phenomena:
Constructing Bosons from Fermions. ElectronElectron Interaction via LatticeCooper Pairs, BCS
Wavefunction. Excitation Spectrum of a Superconductor. GinzburgLandau Theory and London Equation.
Meissner Effect. TypeII Super conductorsCharacteristics Length. Josephson Effect. High Temperature Super
Conductors. (8L)
PAPER 305 [50 Marks]
Computer application practical
PAPER 306 [50 Marks]
Special practical I (List of experiments provided)
SEMESTER IV (300 MARKS)
PAPER 401
Unit I: Statistical Mechanics II [25 Marks]
1. Ideal quantum systems: (a)Properties of ideal Bose gas. Bose-Einstein condensation.
Transition in liquid He4, Superfluidity in He
4. Photon gas. Planck’s radiation law. Phonon gas. Debye’s
theory of specific heat of solids. (b) Properties of ideal Fermi gas: Review of the thermal and electrical
23
properties of an ideal electron gas. Landau levels, Landau diamagnetism. White dwarf and Neutron stars.
(10 L)
2. Strongly interacting systems. Ising model. Idea of exchange interaction and Heisenberg Hamiltonian. Ising
Hamiltonian as a truncated Heisenberg Hamiltonian. Exact solution of one-dimensional Ising system (Matrix
method). Bragg-William’s approximation (Mean field theory) and the Bethe-Peierls approximation.
(6 L)
3. Phase transition: General remarks. Phase transition and critical phenomena. Critical indices. Landau’s order
parameter theory of phase transition. (4 L)
4. Thermodynamic fluctuations. Spatial correlations in a fluid. Brownian motion: Einstein-Smoluchowski’s
theory. (5 L)
Books Recommended
(1) S. Bowley: Introductory Statistical Mechanics (Oxford University Press).
(2) R. Pathria: Statistical Mechanics
4) S. Salinas: Introduction to Statistical Mechanics..
(6) L. Kadanoff: Statistical Mechanics (World Scientific).
Unit II: Astrophysics [25 MARKS]
1. Introduction: Astrophysics and Astronomy. Celestial coordinate systems (Sun-Earth system, Galactic
coordinate system). (2 L)
2. Stellar Structure and Evolution: (i) Star formation. Stellar Magnitudes. Classification of stars. H-D
classification. Saha’s equation of ionization. Hertzsprung-Russel (H-R) diagram. (ii) Gravitational energy,
Virial theorem, Equations of stellar structure and evolution. (iii) Pre-main sequence evolution, Jeans criteria
for star formation, fragmentation and adiabatic contraction, Evolution on the main sequence, Post main
sequence evolution, Polytropic Models. Lane-Emden equation. Simple stellar models. Eddington’s model and
Homologous model, Convective and Radiative stars, Pre-main sequence contraction: Hayashi and Henyey
tracks. (8 L)
3. Nuclear Astrophysics: Thermonuclear reactions in stars, pp chains and CNO cycle. Solar Neutrino
problem. Thermonuclear reactions. Helium burning and onwards. Nucleosynthesis beyond iron, r- and s-
processes. (3 L)
4. Stellar objects and stellar explosions. Brief discussions on: Galaxies, Nebulae, Quasars, Brown dwarfs, Red
giant stars, Nova, Supernova. (2 L)
24
5. Gravitational collapse and relativistic astrophysics: Newtonian theory of stellar equilibrium. White dwarfs.
Electron degeneracy and equation of states. Chandrasekhar limit. Mass-radius relation of WD. Neutron stars.
Spherically symmetric distribution of perfect fluid in equilibrium. Tolman-Oppenheimer-Volkoff equation,
Mass-radius relations of NS. Pulsars, Magnetars, Gamma ray bursts. Black holes: Collapse to a black hole
(Oppenheimer and Snyder), event horizon, singularity.
(7 L)
6. Accretion disks: Formation of accretion disks. Differentially rotating systems in astrophysics. Disk
dynamics. Steady disks. Disk formation in close binary systems through mass transfer. Accretion onto
compact objects (Black holes and Neutron Stars). (3 L)
Books Recommended:
(1) V. Bhatia: Textbook of Astronomy and Astrophysics (Narosa).
(2) K. Abhyankar: Astrophysics – Stars and Galaxies (University Press)..
(3) T. Padmanavan: Theoritical Astrophysics (VoL.I-III) (Cambridge University
Press).
(4) S. Shapiro and S. TeukoLky: Black Holes, White Dwarfs and Neutron Stars (John
Wiley).
(5) E. Kolb and M. Turner: The Early Universe (Addision-Wesley Reading).
(6) J.V.Narlikar: The Structure of the Universe (Oxford University Press)
PAPER 402
Unit I: Advanced Quantum Mechanics [25 Marks]
1. Relativistic quantum mechanics. The Klein-Gordon equation. Covariant notation. Probability density.
Negative energy solution. The Dirac equation. Properties of the Dirac matrices. The Dirac particle in an
electromagnetic field. The magnetic moment of the electron. (5 L)
2. Covariant form of the Dirac equation. Lorentz covariance. Rotation, parity and time reversal operations on
the Dirac wavefunction. The Γ5 matrix and its properties. Plane wave solutions of the Dirac equation and
their properties. Energy and projection operators. Dirac’s hole theory.
(4L)
4. Non-relativistic limit of the Dirac equation. Large and small components. Spin-orbit interaction from Dirac
equation. Foldy-Wouthuysen transformations for a free particle and for a particle in a field. Electon in a
25
central electrostatic potential. Hyperfine structure of hydrogenic atoms.
(4L)
5. Concept of field. Lagrangian dynamics of classical fields. Euler-Lagrange equation. Lagrangians and
equations of motion of fundamental fields. Noether’s theorem. Conserved currents and charges. Energy-
momentum tensor and energy of fields. (4 L)
6. Canonical quantization and particle interpretation of the real Klein-Gordon field. Normal ordering.
Introduction of antiparticle. Charge of complex Klein-Gordon field. (3 L)
7. Interacting fields (mainly electromagnetic interaction). A system of interacting electrons and photons.
Covariant perturbation theory. Derivation of the S-matrix operator. Time-ordering. Application to Compton
scattering. Wick’s theorem (statement only). Enumeration of terms of S-matrix element and corresponding
Feynman diagrams. (5L)
Books Recommended:
1. J. Bjorken and S. Drell: Relativistic Quantum Mechanics (McGraw-Hill).
2. J. Bjorken and S. Drell: Relativistic Quantum Fieldss (McGraw-Hill).
3. J. Sakurai: Advanced Quantum Mechanics (Addison-Wesley).
4. A. Lahiri and P. Pal: A First Book of Quantum Field Theory (Narosa).
5. T-Y Wu and W-Y Hwang: Relativistic Quantum Mechanics and Quantum Fields
(Allied Publishers).
6. C. Itzyksen and J. Zuber: Quantum Field Theory (McGraw-Hill).
7. L. Ryder: Quantum Field Theory (Cambridge University Press).
Unit II: Advanced Optics [25 Marks]
1. Coherence of light. Mutual coherence function. Complex degree of coherence. Quasi-monochromatic fields
and visibility. Spatial coherence of ordinary and laser light. Photon statistics. Poissonian photon statistics.
Classification of light by photon statistics. Photon statistics of thermal and laser sources. Brown-Twiss
correlations. Photon bunching and antibunching. (6L)
2. Historical background of laser. Einstein coefficients and stimulated light amplification. Gain and feedback.
Threshold. Photon rate equations. Population rate equations. Population inversion. Creation of population
26
inversion in three level and four level lasers. Small-signal gain and saturation. Pumping processes.
(6 L)
3. Basic Laser Systems. Gas Laser. CO2 laser. Solid State Laser: Host material and its characteristics. Doped
ions. Nd:YAG laser. Liquid laser. Dye laser. Semiconductor laser.
(3 L)
4. Nonlinear Optics. Origin of nonlinearity. Nonlinear optical materials. Nonlinear polarization. Nonlinear
susceptibilities. Self-focussing. Self-phase modulation. Second harmonic generation. Phase matching. Three-
wave mixing. Parametric amplification and oscillation (3 L)
5 Fibre optics. Dielectric slab waveguide. Modes in the symmetric slab waveguide. TE and TM modes.
Modes in the asymmetric slab waveguide. Coupling of the waveguide (edge, prism, grating). Dispersion and
distortion in the slab waveguide. Integrated optics components (active, passive). Optical fibre waveguides
(step index, graded index, single mode). Attenuation in fibre. Couplers and connectors. LED. Injection laser
diode (double heterostructure, distributed feedback).
(5 L)
6. Detection of optical radiation. Photon detectors (photoconductive, photo voltaic detector and photoemissive
detectors). p-i-n photodiode. APD photodiode. (2 L)
Books recommended:
(1) O. Svelto: Principles of lasers (Springer).
(2) M. Fox: Quantum Optics (OUP)
(3) P. Miloni and J. Eberly: Laser Physics (John Wiley).
(4) A. Ghatak and K. Thyagarajan: Introduction to Fibre Optics.
(5) D. Mills: Nonlinear Optics (Narosa).
PAPER 403
Unit I: Nonlinear Dynamics [25 Marks]
1. Importance of nonlinearity. Phase space. Framework for the study of dynamics in state space. Systems
described by first-order differential equations. Autonomous and nonautonomous systems. The no-intersection
theorem. Dissipative systems and attractors. One-dimensional state space. Fixed points and stability.
Linearization near fixed points. Lyapunov exponent. Trajectories in a one-dimensional state space. Phase
27
portrait. Simple illustrative examples. Population growth. Double-well potential.
(6 L)
2. Two-dimensional state space. Types of fixed points. Brusselator model. Dynamics and complex
characteristic values. Dissipation and the divergence theorem. Jacobian matrix for characteristic values. Limit
cycles. Poincaré sections and the stability of limit cycles. Poincaré-Bendixson theorem.
(5 L)
3. Bifurcations. Saddle-node and repellor-node bifurcations. Supercritical and subcritical pitchfork
bifurcations. Overdamped bead in a rotating hoop. Bifurcations in two dimensions. Limit cycle bifurcations.
Hopf bifurcation. (4 L)
4. Three-dimensional state space. Routes to chaos. Period doubling. Quasi-periodicity. Intermittancy. Lorenz
model, Simple properties of the Lorenz equations, (4 L)
5. Classical chaos. Periodic motion. KAM theorem. Chaotic trajectories and Lyapunov exponents. Poincaré
maps. Hénon-Heiles Hamiltonian. Driven damped harmonic oscillators. The logistic equation. Fractals and
dimensionality. (6L)
Books Recommended:
(1) R. Hilborn: Chaos and Nonlinear Dynamics (Oxford University Press).
(2) S. Strogatz: Nonlinear Dynamics and Chaos (Addison-Wesley).
(3) J. Bhattacharjee: Nonlinear Dynamics Near and Far From Equilibrium (Hindustan
Book Agency).
(4) H. Goldstein, C. Poole and J. Safko: Classical Mechanics (Pearson)
Unit II [Elective: A/B/C] [25 Marks]
A. Physics of Liquid Crystal:
1. Structure and classification of mesophases. Recent interests in liquid crystals; X-ray analysis of liquid
crystals; Measurement of nematic order parameter by NMR;.
(4 L)
2. Molecular theory of nematic liquid crystals: Symmetry and order parameter; Molecular potential;
Distribution function; Nematic -isotropic (N-I) phase transitioni, Maier-Saupe theory; Generalized
mean field theory; The even-odd effect, Onsager equation. Molecular theory of smectic A liquid
crystals: Millan's theory. (10 L)
28
3. Elastic continuum theory of liquid crystals: General expression of free energy of a
deformed nematic liquid crystal; Franck's elastic constants; Distortion due to external
electric or magnetic field. (6 L).
4. Landau's theory of phase transition (3L)
5. Liquid crystal displays (2L)
Books recommended:
1. E.B. Priestley, P.J. Wojtowich and P. Sheng: Introduction to Liquid Crystals
2. P.G. de Gennes: Physics of Liquid Crystal
3. S. Chandrasekhar: Liquid Crystals
4. P.J. Collings and M. Hand: Introduction to Liquid Crystals
B. Elements of General Relativity and Cosmology
1. Review of special theory of relativity: Poincare and Minkowski’s 4-dimensional formulation. Geometrical
representation of Lorentz transformations in Minkowski’s space. Length contraction. Time dilation.
Causality. Time-like and space-like vectors. Newton’s second law of motion expressed in terms of 4-vectors.
(4 L)
2. Tensor calculus: Idea of Euclidean and non-Euclidean space. Meaning of parallel transport and covariant
derivatives. Geodesics and autoparallel curves. Curvature tensor and its properties. Bianchi Identities.
Vanishing of Riemann-Christoffel tensor as the necessary and sufficient condition of flatness. Ricci tensor.
Einstein tensor. (5 L)
3. Einstein’s field equations: Inconsistency of Newtonian gravitation with the special theory of relativity.
Principles of equivalence. Principle of general covariance. Metric tensors and Newtonian Gravitational
potential. Logical steps leading to Einstein’s field equations of gravitation. Linearised equation for weak
fields. Poisson’s equation. (4 L)
4. Applications of general relativity: Schwarzschild’s exterior solution. Singularity. Event horizon and black
holes. Isotropic coordinates. Birkhoff’s theorem. Observational tests of Einstein’s theory.
(4 L)
5. Gravitational Collapse and Black Holes: Brief discussions on: White dwarfs, Neutron stars, static and
rotating black holes (Schwarzschild and Reissner-Nordstrom). Kerr metric (derivation not required), event
29
horizon, extraction of energy by Penrose process. Kerr-Neumann Metric (no derivation). No hair theorem.
Cosmic censorship hypothesis. (3 L)
6. Cosmology: Cosmological principles. Weyl postulates. Robertson-Walker metric (derivation is not
required). Cosmological parameters. Static universe. Expanding universe. Open and closed universe.
Cosmological red shift. Hubble’s law. Olber’s paradox. Brief discussions on: Big bang, Early universe
(thermal history and nucleosynthesis), Cosmic microwave background radiation, Particle horizon.
(5 L)
Books Recommended:
(1) J. Narlikar: General Relativity and Cosmology (MacMillion).
(2) S. Weinberg: Gravitation and Cosmology: Principles and Applications of the
General Theory of Relativity (Wiley).
(3) P. G. Bergmann- Introduction to Theory of Relativity (Prentice-Hall).
(4) J. Narlikar: Introduction to Cosmology (Cambridge Univ. Press).
(5) A. Roychaudhuri, S. Banerjee and A. Banerjee: General Relativity, Astrophysics
and Cosmology (Springer-Verlag).
(6) S. Banerji and A. Banerjee: General Relativity and Cosmology (ELevier)
(7) W. Rosser: Introduction to the Theory of Relativity
C. Plasma Waves and Instabilities
1. Theory of plasma waves:
Derivation of dielectric tensor and dispersion relation for cold uniform magnetized plasma. Cut off and
resonance. Alfven waves, Ion and electron cyclotron waves, Lower hybrid waves: Mode conversion,
accessibility condition, Ray Tracing, Whistlers, warm plasma modes. Ion acoustic and Langmuir waves.
Plasma heating method. ( 10 L)
2. Magnetohydrodynamic treatment of plasmas.
Equilibrium equations, Approximations, magnetic surfaces, surface quantities, Relation among sufface
quantities, Flux co-ordinates, magnetic field representation. Gard-Shafranov (G-S) equation and examples
of G-S solutions. Interchange, Sausage and Kink instabilities.
( 10 L)
30
3. Nonlinear Phenomena: Large amplitude electron plasma oscillation, Exact solution in Lagrangian
variable, extension of the model. Derivation Korteweg- de Vries equation for nonlinear sound wave.
Solitary wave solution. Nonlinear drift-waves. ( 5 L)
PAPER 404 [Special Paper: A/B/C]
A. Advanced Electronics II [50 Marks]
1. Review of CW Modulation Technique: Linear modulation DSB, SSB, VSB, QAM techniques, Exponential
modulation FM and PM; AM and FM modulators and demodulators.
(5 L)
2. Pulse Modulation and Demodulation Techniques : Sampling the rein PAM, PWM, PPM, Pulse code
modulation – coding technique. Modulation and demodulation.
(5 L)
3. Digital Modulation Techniques : Principles of ASK, FSK, PSK, DPSK, QPSK, MSK. Modulators and
demodulators. (5 L)
4. Effect of Noise on Communication System: Characteristics of additive noise; Performance of AM, FM and
PCM receivers in the face of noise. Multi-path effect.
(5 L)
5. Elements of Information Theory: Information, average information, information rate, Effect of coding on
average information per bit. Shanon’s theorem; Channel capacity. Optimum modulation system in AWGN
channel. (5 L)
6. TV Systems: Color TV standards – NTSC, PAL, SECAM; Transmission format of intensity and color
signal. Transmitter and receiver systems of broadcast TV.Advanced
TV. Cable TV. (5 L)
7. RADAR System: Basic pulsed radar system – modulators, duplexer indicators, radar antenna CW radar.
MTI radar FM radar; chirped pulse radar. (4 L)
8. Optical Communication: Fibre optic communication systems. Power budget equation; Multiplexing.
Quantum limit. Incoherent reception. Signal-to-noise ratio calculation. Basics of coherent techniques in FOC.
(4 L)
9. Satellite Communication: Orbits, Station keeping. Satellite attitude. Path loss calculation. Link calculation.
Multiple access techniques. Transponders. Effects of nonlinearity of transponders.
(4 L)
31
10. Specialised Communication Systems: Mobile Communication – Concepts of cell and frequency reuse
description of cellular communication standards; Pagers. Computer communication – Types of networks.
Circuit message and packet switched networks. Features of network, design and examples of ARPANET,
LAN, ISDN, Medium access techniques – TDMA, FDMA, ALOHA, Slotted ALOHA, CSMA/CD. Basics of
protocol.
(8 L)
Books Recommended
1. A. Carlson: Communication Systems.
2. S. Haykin: Communication Systems (Wiley).
3. D. Roddy and J. Coolen: Electronic Communications.
4. Franz and Jain: Optical Communication Systems (Narosa).
5. A. Dhake: Television and Video Engineering (TMH).
6. Gulati: Monochrome and Color TV.
7. Kennedy and Davis; Electronic Communication Systems (TMH).
8. Taub and Schilling: Principle of Communication Systems (TMH).
9. B. P. Lathi: Modern Digital and Analog Communication Systems (Oxford).
B. Computational Physics II [50 Marks]
1. Applications in Quantum Mechanics: Numerical solution of Schrodinger equation- square well, particle in
a box, harmonic oscillator, hydrogen atom; Applications in time independent perturbation theory.
(25L)
2. Applications in Statistical Mechanics: Monte Carlo simulation; Ising model; Random walk problems;
Molecular dynamics simulation. (25L)
C. Condensed Matter Physics II [50 Marks]
I. Electronic Quasiparticles in Solids:
Quasiparticles, Effective Mass, Basic Behaviour of Semiconductors, Band Bending and Heterojunctions.
Quantum Confinement: Density of States in Quantum confined Systems Low dimensional systems),
Excitons in Quantum Structures, Superlattices, Disorder in quantum Confined Systems, Two Dimensional
Electron Gas. Landau Levels and quasiparticles in Magnetic Field: Density of States in Landau Levels, De
32
Hassvan Alphen and Shubnikov De Hass Oscillations, Integer Quantum Hall Effect, Fractional Quantum
Hall Effect and Higher – Order Quasiparticles. (8L)
II. Ineractions of Quasiparticles & Transport Phenomena in Solids: Electron Phonon Interactions:
Deformation Potential Scattering, Piezoelectric Scattering, Fröhlich scattering. ElectronPhoton Interactions:
Optical Transitions between Semiconductor Bands, Direct & Indirect Transitions, Joint Density of States.
PhononPhonon Interactions. ElectronElectron Interactions: Semiclassical Estimation of Screening Length.
The Relaxation Time Approximation and Diffussion Equation. The Boltzmann Transport equation. Thermal
Conductivity, Electrical Conductivity and Magnetoresistance in Two Band Model. Drift of Defects and
Dislocations – Plasticity. (8L)
III. The Complex Susceptibility & Dielectric Properties of Materials: A Microscopic view of the Dielectric
Constant. KramersKronig Relation. The Quantum Mechanical Oscillator, Dielectric Functions. Polaritons.
Nonlinear Optics and PhotonPhoton Interactions: SecondHarmonic Generation and ThreeWave Mixing,
HigherOrder Effects. AcoustoOptics and PhononPhonon Interactions. Raman Scattering.
(6L)
IV. Growth, Characterization and Phase Diagrams of Materials: Classification of materials (crystalline,
amorphous, nanomaterials, ceramics, liquid crystals and polymers). Growth: Processes for crystal growth,
doping techniques of elemental and compound semiconductors; Growth processes (Physical and Chemical
Vapor Deposition) and fundamentals of thin films; Recent developments in material processes.
Characterization: Diffraction techniques – Xray Diffraction, Neutron Diffraction; Electron Microscopy –
Transmission Electron and Scanning Electron Microscopy; Optical methods – FTIR, Raman Spectroscopy,
UV – VIS – NIR – IR; Surface techniques – AFM, STM, Chemical ESCA, AES and RBS; Thermal methods
– DTA, TGA, DSC; Other techniques – ESR, NMR, Mössbauer and Positron annihilation. Phase Diagrams:
Phase Rule, Single component, Binary systems and Lever Rule. (9L)
V. Liquid Crystals: Isotropic. Nematic and Cholesteric Phases. SmecticsA and –C. Hexatic Phases. Discotic
Phases. Lyotropic Liquid Crystals and microemulsions. (4L)
VI. NonCrystalline Materials: Microstructure and imperfections. Diffusion in solids and related phenomena.
Noncrystalline and glassy materials – Structure, Thermodynamics, Glass transition and related models,
tunneling states, Specific heat estimation, Two –level system. Amorphous semiconductors – Electrical
properties, magnetic properties, switching and device applications. (7L)
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VII. Nanostructure Materials and Carbon NanoTubes:
Properties of Individual Nanoparticles. Quantum Wells, Wires and Dots. Size and Dimensionality Effects.
Preparation and Characterization of Quantum nanostructures. Applications of nanostructures. SelfAssembly
and catalysis. Carbon Nanostructures: carbon Clusters & Fullerenes. Carbon Nanotubes: fabrication, Structurs
& Electronic Properties, Application of carbon Nanotubes. Nanostructured Ferromagnetism, Nanocarbon
Ferromagnets, Giant and Colossal Magnetoresistance. Ferrofluids. (8L)
PAPER – 405: [50 Marks]
Special Practical II ( List of experiments provided)
PAPER – 405 : Project [50 Marks]
( Project work. 35 viva 15)
List of General Practical
(For semester I & II)
1. Study of temperature dependence of resistivity for a given semiconductor using FOUR PROBE SETUP
and determine its energy band gap.
2. Determination of Saturation Magnetization, Retentivity and Coercivity of given Ferromagnetic samples
Using HYSTERESIS LOOP TRACER.
3. Determination of Hall Coefficient of a given semiconductor sample using variable DC magnetic field.
4. 10.Study of the variation of Hall Coefficient of a given extrinsic semiconductor as a function of
temperature using Temperature dependence Hall – effect setup.
5. Determination of the specific charge of an electron by the SOLENOIDAL LENS METHOD / MODIFIED
THOMPSON’S METHOD.
6. Study of LISSAJOUS FIGURES and calibrate an Audio Frequency Oscillator by PHASE CHANGE AND
DIRECT METHOD.
7. Determination of the velocity of ultrasonic wave in a given liquid for a given frequency using MULTI
FREQUENCY ULTRASONIC INTERFEROMETER /LIQUID GRATING METHOD.
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8. Determination of the Lande g factor for the DPPH sample using ELECTRON SPIN
RESONANCE SETUP.
9. Study of absorption spectrum of Iodine vapor using OPTICAL SPECTROMETER
and determine its ( i) Dissociation energy and (ii) Anharmonicity constant.
10. Determination of the thickness of a given transparent plate with the help of JAMIN’S
INTERFEROMETER.
11. Determination of the refractive index of a given transparent thin film using MICHELSON
INTERFEROMETER.
12. Determination of the average wavelength and the difference between the wavelength of its two
components of sodium light used as source employing MICHELSON INTERFEROMETER.
12. Study of atomic spectroscopy using ZEEMAN EFFECT.
13. Study of Polarization of light using LASER BEAM.
14. Determination of AC Conductivity and Dielectric Constants of Composites Materials by LCR Bridge.
15. Study of Photoconductivity of semiconductors.
List of Electronics Practical
(For semester I & II)
1. To design and study an amplifier with an Op-amp.
2. To design and study an oscillator with an Op-amp.
3. To design and study a voltage follower circuit with an Op-amp
4. Construct a sawtooth wave generator using UJT for different frequencies. Determine VP, VV and ,
symbols having the usual meanings. η For a fixed C, vary R (5 values) and Draw the TR graph. Plot the
theoretical TR graph on the same graph paper. Obtain two such sets.
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5. Construct a sawtooth wave generator using UJT for different frequencies. Determine VP, VV and , symbols
having the usual meanings. η For a fixed R, vary C (5 values) and Draw the TC graph. Plot the theoretical TC
graph on the same graph paper. Obtain two such sets.
6. Design an astable multivibrator with two transistors for a fixed given frequency (1.0 KHz). Assume
Vc(sat)=0.2 volt, Ic(sat)=5 mA, hFE(min)=100 and VBE(sat)=0.6 volt. Compare the experimentally obtained
frequencies with the required theoretical values. Using this multivibrator design a VCO and draw its transfer
characteristics. From this plot calculate the VCO sensitivity.
7. Design the following RC active filters: (a) Low Pass, having cut off frequency 10 KHz. (b) Band Pass,
having Centre frequency 2.8 KHz and bandwidth 3.2 KHz. Draw separate frequency response curves and
compare the theoretical and experimental results.
8. Design the following RC active filters:
(a) High Pass, having cut off frequency 5 KHz.
(b) Band Stop, having Centre frequency 3.4 KHz and bandwidth 3.0 KHz.
Draw separate frequency response curves and compare the theoretical and experimental results.
9.Design the following using NAND gates only:
(a) SR FlipFlop with the provision of clock (enable input). Study the output for different combinations of S
and R.
(b) Convert the above to clocked D Flip Flop.
(c) Design a clocked JK FlipFlop and study the results of different combinations of J, K and clock.
Note the drawback of the experimental circuit, if any and suggest a suitable circuit to remove the drawback
with proper explanation.
10. Design a transistor CE amplifier of midband gain 50 and study its performance in
the following way:
(a) Test the linearity of inputoutput variations of a voltage signal of suitable fixed frequency and show it
graphically.
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(b) For fixed amplitude of input ac signal within the linear region, study the frequency response with
an external bypass capacitor at the output.
Plot the gain frequency graph and determine the bandwidth of the amplifier.
11. (a) Study the performance of AM modulator circuit by considering three different values of modulating
signal amplitude and frequency. Determine modulation index in each case.
(b) Study the performance of AM demodulator circuit by considering three different values of modulating
signal amplitude and frequency. Write down your observations clearly.
12. Study the performance of Passive T type Low Pass and High Pass filters considering three different values
of load. Draw separate frequency response curves for Low Pass and High Pass filters.
List of Advanced Electronics (I &II) Experiments
(For semester III & IV)
1. A. Experiments with OPAMP and timer IC Waveform generators – square, triangular, sawtooth
2. Solution of simultaneous algebraic equations
3. Astable and monostable multivibrator with variable frequency and duty cycle using 555 IC.
4. Voltagecontrolled oscillator with 555 IC
5. Simple microprocessor programs, for example:
(a) Average of some numbers
(b) Testing even/odd
(c) Addition of 2byte numbers
(b) Multiplication of two 8bit numbers
(c) Division of two 8bit numbers with (a) quotient only (b) both quotient and
reminder
(d) Testing for A=B, A>B and A<B conditions for two given numbers A and B
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(e) Sum of 10 even (odd) numbers
(f) Factorial of a given number
(g) To check the parity of a given number
(h) To sort out the largest/smallest of a given set of numbers
(i) To arrange a given set of numbers in ascending/descending order
(j) Configuring delay programs for prescribed period
(k) Display programs – displaying in address field, data field and both
6. Characteristics of solar cell with variation in (i) waveband (ii) distance and (iii) area of exposure and
calculation of parameters
7. Optical communication with LED, photodiode and optical fibers
8. Experiments on digital electronics
(a) Fabrication of shift register with JK master slave flip-flops and study of series
and parallel in/out operations
(b) Fabrication of counters of different modulus using JK master slave flip-flops.
Use of 7490 counter chip
(c) R2R ladder D/A converter (4bit and 8bit)
(d) Use of 7483 adder chip as adder, subtractor and both
(e) Diode ROM with decoder
(f) Use of 7segment display
9. Microprocessor Interfacing
(a) Configure port A/port B/port C as output ports
(b) Generate square waves (symmetric, asymmetric and variable amplitude) using 8255 IC and display in
CRO
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(c) Generate triangular wave/saw tooth wave using 8255 IC and display in CRO
(d) Control system, such as: (i) Stepper motor controller (ii) Use of relay module
(e) Use of D/A and A/D converters
(f) Introductory use of microcontroller
10. Experiments on microwave
(a). Familiarity with microwave components and assembling those
(b) Gunn diode characteristics
(c) Use of waveguide and horn antenna in microwave communication.
Advanced Experiments (Condensed Matter Physics I &II)
1. Determination of Space Group and Crystal Structure of a Single Crystal Material
by Laue Diffraction Method.
2. Determination of Crystal Structure and Lattice Parameters of a Polycrystalline
Material by Powder Diffraction (Debye Scherrer) Method.
3. Determination of Hall Effect & Magnetoresistance of Polycrystalline Bismuth
Sample.
4. Determination of Magnetic Susceptibility of Paramagnetic Salts by Guoy Balance
Method.
5. Determination of AC Conductivity and Dielectric Constants of Composites Materials by LCR Bridge.
6. Study of Dielectric Constants of Ferroelectric Crystals at Elevated Temperatures and determine the Curie
Temperature.
7. Study of FCenters of Xray Irradiated Alkali Halides (KCl & KBr) Samples.
8. Study of the Nature of Band Gap and Determination of Optical Constants (n, k) of Semiconductor
(Crystalline and Amorphous) Thin Films using UVVIS (Dual and Single beam) Spectrophotometer.
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9. FTIR Study of Si Based Oxide/ Carbon NanoComposites.
10.Study of the variation of Hall Coefficient of a given extrinsic semiconductor as a
function of temperature using Temperature dependence Hall – effect setup.
11.Study of the electrical properties of given thin films of different materials (metal,
insulator and semiconductor) using Four – Probe Setup.