Syllabus for Courses in M.Sc. in Physics/Post-graduate Physics/    M. Sc. (Research)

           Mathematical Methods in Physics (4 credits)

Linear vector spaces

Linear vector space, dual vector space, inner product spaces. Linear (in)dependence, bases, dimension. Linear operators, matrices for linear operators. Eigenvalues and eigenvectors. Similarity transformation, (matrix) diagonalization, Gram-Schmidt algorithm. Special matrices: normal, Hermitian and unitary matrices. Cauchy-Schwarz and triangle inequalities.

Complex analysis

Complex numbers, variables and functions. Complex analyticity, Cauchy-Riemann conditions. Classification of singularities. Cauchy's theorem. Residues. Branch points and branch cuts. Evaluation of definite integrals. Taylor and Laurent expansions. Fourier Series, Fourier and Laplace Transforms.

Analytic continuation, Gamma function, zeta function. Method of steepest descent. Riemann Sheets

Ordinary Differential Equations and Special Functions

Linear ordinary differential equations, regular and (ir)regular singular points. Series solution, linear (in)dependence, Wronskian, second solution. Examples: Hypergeometric function, Bessel functions and classical polynomials (Legendre, Hermite and Laguerre). Sturm-Liouville problem, expansion in orthogonal functions. Inhomogenous equation and Green’s function.

Partial Differential Equations

Laplace and Poisson equation (with particular emphasis on solving boundary value problems). Wave equation. Heat Equation. Separation of variables and solution in different coordinates. Green’s function approach.

References:

1. G.B. Arfken, Mathematical Methods for Physicists, Elsevier
2. P. Dennery and A. Krzywicki, Mathematics for Physicists, Dover
3. S.D. Joglekar, Mathematical Physics: Basics (Vol. I) and Advanced (Vol. II),

Universities Press

4. V. Balakrishnan, Mathematical Physics, Ane Books
5. A.W. Joshi, Matrices and Tensors in Physics, New Age Publishers
6. M.R. Spiegel, Complex Variables, McGraw-Hill
7. R.V. Churchill and J.W. Brown, Complex Variables and Applications,

McGraw-Hill

8. P.M. Morse and H. Feshbach, Methods of Theoretical Physics (Vol. I & II),

Feshbach Publishing

                Introductory Classical Mechanics (4 credits)

Lagrangian and Hamiltonian mechanics

Constraints and generalized coordinates. Calculus of variation, Euler-Lagrange equations. Hamilton's principle of least action, Lagrange's equations of motion. Cyclic coordinates, symmetries and conservation laws, Noether’s theorem. Hamilton's equations of motion, canonical variables. Canonical transformations, generating functions. Poisson brackets.

Two-body central force problem

Equation of motion and first integrals. Kepler problem. Classification of orbits. Satellites and inter-planetary orbits. Scattering in central force field.

Small oscillations

Linearization of equations of motion. Normal coordinates. Damped and forced oscillations. Anharmonic terms, perturbation theory.

Rigid body dynamics

Rotational motion, moments of inertia, principal axes, torque. Euler’s theorem, Euler angles. Symmetric top.

Special theory of relativity

Motivation. Postulates of special theory of relativity. Lorentz transformation. Space- time diagram. Time dilation and length contraction. Equivalence of mass and energy. Addition of velocities. Doppler effect. Paradoxes. Four-vectors, contra- and covariant vectors.

Coordinate, velocity and momentum four-vectors. Tensors.

Hamiltonian-Jacobi theory, integrability and chaotic dynamics

Hamilton-Jacobi theory, action-angle variables, integrable system. Phase plots, fixed points and their stabilities. Introduction to chaotic dynamics.

References:

1. H. Goldstein, C.P. Poole and J.F. Safko, Classical Mechanics, Addison- Wesley
2. N.C. Rana and P.S. Joag, Classical Mechanics, Tata McGraw-Hill
3. J.V. Jose and E.J. Saletan, Classical Dynamics: A Contemporary Approach,Cambridge University Press
4. L.D. Landau and E.M. Lifshitz, Mechanics, Butterworth-Heinemann
5. I.C. Percival and D. Richards, Introduction to Dynamics, Cambridge University Press
6. R.D. Gregory, Classical Mechanics, Cambridge University Press
7. A.P. French, Special Relativity, W.W. Norton
8. E.F. Taylor and J.A. Wheeler, Spacetime Physics: Introduction to Special Relativity,

W.H. Freeman

Quantum Mechanics I (4 credits)

Introduction and formalism

Review of empirical basis, wave-particle duality, electron diffraction. Postulates of quantum mechanics: state vector, Dirac (bra-ket) notation, probability interpretation, physical observables and linear operators, eigenvalues and measurement. Operators as matrices: Heisenberg-Born-Jordan description.

Commutation relations. Uncertainty principle. Correspondence principle, Ehrenfest

theorem.

Quantum dynamics

Time-dependent Schrödinger equation. Stationary states and their significance. Time- independent Schrödinger equation. Two-state quantum systems.

Density matrix.

Schrödinger equation for one-dimensional systems

Free-particle, periodic boundary condition. Wave packets. Square well potential. Transmission through a potential barrier. Gamow theory of alpha-decay. Field induced ionization, Schottky barrier.

Simple harmonic oscillator: solution by wave equation and operator method. Coherent states. Charged particle in a uniform magnetic field. Landau levels.

Spherically symmetric potentials

Separation of variables in spherical polar coordinates. Orbital angular momentum, parity. Spherical harmonics. Free particle in spherical polar coordinates. Spherical well. Hydrogen atom.

Identical particles

Indistinguishability, symmetric and anti-symmetric wave functions, incorporation of spin, Slater determinants, Pauli exclusion principle. Spin-statistics relation.

References:

1. L.I. Schiff, Quantum Mechanics, McGraw-Hill
2. R. Shankar, Principles of Quantum Mechanics, Springer
3. D.J. Griffiths, Introduction to Quantum Mechanics, Cambridge University Press
4. N. Zettili, Quantum Mechanics: Concepts and Applications, Wiley
5. J.S. Townsend, A Modern Approach to Quantum Mechanics, Viva Books
6. E. Merzbacher, Quantum Mechanics, John Wiley and Sons
7. F. Schwabl, Advanced Quantum Mechanics, Springer
8. A. Das, Lectures on Quantum Mechanics, Hindustan Book Agency
9. M. Le Bellac, Quantum Physics, Cambridge University Press
10. J. J. Sakurai, Modern Quantum Mechanics, Pearson
11. S. Flügge, Practical Quantum Mechanics, Springer
12. K. Gottfried and T.-M. Yan, Quantum Mechanics: Fundamentals, Springer
13. R.P. Feynman, Feynman Lectures on Physics (Vol. III), Addison-Wesley
14. C. Cohen-Tannoudji, B. Diu and F. Laloe, Quantum Mechanics (Vols. I and II),

Wiley

15. A. Messiah, Quantum Mechanics (Vols. I and II), Dover

Classical Electrodynamics (4 credits)

Brief Review of Electrostatics and Magnetostatics

Coulomb’s law, action-at-a distance vs. concept of fields, Poisson and Laplace equations, formal solution for potential with Green's functions, boundary value problems; multipole expansion; Dielectrics, polarization of a medium; Biot-Savart law, differential equation for static magnetic field, vector potential, magnetic field from localized current distributions; Faraday's law of induction; energy densities of electric and magnetic fields.

Maxwell’s Equations

Maxwell’s equations in vacuum. Vector and Scalar potentials in electrodynamics, gauge invariance and gauge fixing, Coulomb and Lorenz gauges. Displacement current. Electromagnetic energy and momentum. Conservation laws. Inhomogeneous wave equation and its solutions using Green’s function method.

Electromagnetic Waves

Plane waves in a dielectric medium, reflection and refraction at dielectric interfaces. Frequency dispersion in dielectrics and metals. Dielectric constant and anomalous dispersion. Wave propagation in one dimension, group velocity. Metallic wave guides, boundary conditions at metallic surfaces, propagation modes in wave guides, resonant modes in cavities. Dielectric waveguides. Plasma oscillations.

Covariant formulation

Four-vectors, contra- and covariant vectors. velocity and momentum four-vectors, Electromagnetic field tensor. Maxwell's equations in tensor notation. Covariant formulation of Maxwell’s equations. Transformation of electromagnetic field.

Motion of charged particles in electromagnetic fields

Motion of charged particle in electromagnetic field, Lorentz force, Time varying E and B fields, Adiabatic invariants. Relativistic Lagrangian of charged particles in electromagnetic fields.

Radiation

EM Field of a localized oscillating source. Fields and radiation in dipole and quadrupole approximations. Radiation by moving charges, Lienard-Wiechert potentials, total power radiated by an accelerated charge, Lorentz formula.

References:

1. D.J. Griffiths, Introduction to Electrodynamics, Prentice Hall
2. J.D. Jackson, Classical Electrodynamics, Wiley
3. A. Das, Lectures on Electromagnetism, Hindustan Book Agency
4. J.R.   Reitz,    F.J.   Milford   and    R.W.   Christy, Foundations  of    Electromagnetic Theory, Addison-Wesley
5. W.K.H. Panofsky and M. Phillips, Classical Electricity and Magnetism, Dover
6. R.P. Feynman, Feynman Lectures on Physics (Vol. II), Addison-Wesley
7. A. Zangwill, Modern Electrodynamics, Cambridge Univ Press
8. A. Sommerfeld, Electrodynamics, Academic Press, Freeman and Co.
9. L. D. Landau and E. M. Lifshitz, Electrodynamics of continuous media, Addison Wesley
10. A.K. Raychaudhuri, Classical Theory of Electricity and Magnetism: A Course of Lectures

(Revised Edition), Hindustan Book Agency

Experimental Physics I (6 credits)

Minimum 10 experiments have to completed in a semester

• • Error analysis
  • G.M Counter
  • Experiments with microwaves
  • Resistivity of semiconductors
  • Work function of Tungsten
  • Hall effect
  • Thermal conductivity of Teflon
  • Susceptibility of Gadolinium
  • Transmission line, propagation of mechanical and EM waves
  • Measurement of e/m using Thomson method
  • Measurement of Planck’s constant using photoelectric effect
  • Michelson interferometer
  • Millikan oil-drop experiment
  • Frank-Hertz experiment
  • Experiments using semiconductor laser

Quantum Mechanics II (4 credits)

Symmetries and conserved quantities

Symmetry operations and unitary transformations, Wigner's theorem. Conservation laws. Space and time translations, rotation. Discrete symmetries: Space inversion, time reversal and charge conjugation. Symmetry and degeneracy.

Angular momentum

Rotation operators, generators of infinitesimal rotation, angular momentum algebra, eigenvalues of J² and Jz and their matrix representations. Pauli matrices

and spinors. Addition of angular momenta, Clebsch-Gordon coefficients. Spherical tensors, Wigner-Eckart theorem.

Approximation methods

Variational methods. (Non-)degenerate perturbation theory. Stark effect, Zeeman effect and other examples. WKB approximation. Tunnelling. Numerical perturbation theory, comparison with analytical results.

Time-dependent perturbation theory

Sudden and adiabatic approximations. Schrödinger, Heisenberg and interaction pictures. Time-dependent perturbation theory. Transition probabilities, Fermi’s golden rule. Beta decay. Interaction of radiation with matter, Einstein A and B coefficients. Time-energy uncertainty relation.

Scattering Theory

Differential scattering cross-section, scattering of a wave packet, integral equation for the scattering amplitude, Dyson series. Born approximation. Method of partial waves, phase shifts. Scattering from central potential. Optical theorem.

Relativistic theory

Klein-Gordon equation. Dirac equation and its plane wave solutions, intrinsic spin and magnetic moment of fermions. Antiparticles. Relativistic corrections to the hydrogen atom.

References:

1. L.I. Schiff, Quantum Mechanics, McGraw-Hill
2. R. Shankar, Principles of Quantum Mechanics, Springer
3. D.J. Griffiths, Introduction to Quantum Mechanics, Cambridge University Press
4. N. Zettili, Quantum Mechanics: Concepts and Applications, Wiley
5. J.S. Townsend, A Modern Approach to Quantum Mechanics, Viva Books
6. E. Merzbacher, Quantum Mechanics, John Wiley and Sons
7. F. Schwabl, Advanced Quantum Mechanics, Springer
8. A. Das, Lectures on Quantum Mechanics, Hindustan Book Agency
9. M. Le Bellac, Quantum Physics, Cambridge University Press
10. J. J. Sakurai, Modern Quantum Mechanics, Pearson
11. S. Flügge, Practical Quantum Mechanics, Springer
12. K. Gottfried and T.-M. Yan, Quantum Mechanics: Fundamentals, Springer
13. R.P. Feynman, Feynman Lectures on Physics (Vol. III), Addison-Wesley
14. C. Cohen-Tannoudji, B. Diu and F. Laloe, Quantum Mechanics (Vols. I and II),

Wiley

15. A. Messiah, Quantum Mechanics (Vols. I and II), Dover

Solid State Physics (4 credits)

Metals

Drude theory, DC conductivity, Hall effect and magneto-resistance, AC conductivity, thermal conductivity, thermo-electric effects, Fermi-Dirac distribution, thermal properties of an

electron gas, Wiedemann-Franz law, critique of free-electron model.

Crystal Lattices

Bravais lattice, symmetry operations and classification of Bravais lattices, common crystal structures, reciprocal lattice, Brillouin zone, X-ray diffraction, Bragg's law, Von Laue's

formulation, diffraction from non-crystalline systems.

Classification of Solids

Band classifications, covalent, molecular and ionic crystals, nature of bonding, cohesive energies, hydrogen bonding.

Electron States in Crystals

Periodic potential and Bloch's theorem, weak potential approximation, energy gaps, Fermi surface and Brillouin zones, Harrison construction, level density. Motion of electrons in

optical lattices.

Electron Dynamics

Wave packets of Bloch electrons, semi-classical equations of motion, motion in static electric and magnetic fields, theory of holes. Quantum Oscillations

Lattice Dynamics

Failure of the static lattice model, harmonic approximation, vibrations of a one-dimensional lattice, one-dimensional lattice with basis, models of three-dimensional lattices, quantization of vibrations, Einstein and Debye theories of specific heat, phonon density of states, neutron scattering.

Semiconductors

General properties and band structure, carrier statistics, impurities, intrinsic and extrinsic semiconductors, equilibrium fields and densities in junctions, drift and diffusion currents.

Magnetism

Diamagnetism, paramagnetism of insulators and metals, ferromagnetism, Curie-Weiss law, introduction to other types of magnetic order.

Superconductors

Phenomenology, review of basic properties, thermodynamics of superconductors, London's equation and Meissner effect, Type-I and Type-II superconductors.

References:

1. C. Kittel, Introduction to Solid State Physics, Wiley
2. N.W. Ashcroft and N.D. Mermin, Solid State Physics, Brooks/Cole
3. J.M. Ziman, Principles of the Theory of Solids, Cambridge University Press
4. A.J. Dekker, Solid State Physics, Macmillan
5. G. Burns, Solid State Physics, Academic Press
6. M.P. Marder, Condensed Matter Physics, Wiley

Introductory Statistical Mechanics (4 credits)

Elementary Probability Theory

Binomial, Poisson and Gaussian distributions. Central limit theorem.

Review of Thermodynamics

Extensive and intensive variables. Laws of thermodynamics. Legendre transformations and thermodynamic potentials. Maxwell relations. Applications of thermodynamics to (a) ideal gas, (b) magnetic material, and (c) dielectric material.

Formalism of Equilibrium Statistical Mechanics

Phase space, Liouville's theorem. Basic postulates of statistical mechanics. Microcanonical, canonical, grand canonical ensembles. Relation to thermodynamics. Fluctuations.

Applications of various ensembles. Equation of state for a non-ideal gas, Van der Waals' equation of state. Meyer cluster expansion, virial coefficients. Ising model, mean field theory.

Quantum Statistics

Fermi-Dirac and Bose-Einstein statistics.

Ideal Bose gas, Debye theory of specific heat, properties of black-body radiation. Bose- Einstein condensation, experiments on atomic BEC, BEC in a harmonic potential.

Ideal Fermi gas. Properties of simple metals. Pauli paramagnetism. Electronic specific heat. White dwarf stars.

Interacting systems

Ising model for ferromagnetism, mean field theory, critical exponents, Landau theory of phase transitions.

References:

1. F. Reif, Fundamentals of Statistical and Thermal Physics, Levant
2. K. Huang, Statistical Mechanics, Wiley
3. R.K. Pathria, Statistical Mechanics, Elsevier
4. D.A. McQuarrie, Statistical Mechanics, University Science Books
5. S.K. Ma, Statistical Mechanics, World Scientific
6. R.P. Feynman, Statistical Mechanics, Levant
7. D. Choudhury and D. Stauffer, Principles of Equilibrium Statistical Mechanics, Wiley- VCH

Computational Physics and Data Science (4 Credits)

Overview

Computer organization, hardware, software. Scientific programming in FORTRAN and/or C, C++ and Python. Typesetting and plotting using Latex and gnuplot, Introduction to Mathematica or Matlab

Numerical Techniques

Sorting, interpolation, extrapolation, regression, finite and infinite series, numerical integration, quadrature, random number generation, linear algebra and matrix manipulations, inversion, diagonalization, eigenvectors and eigenvalues, integration of initial-value problems, Euler, Runge-Kutta, and Verlet schemes, root searching, optimization.

Simulation Techniques

Monte Carlo methods, molecular dynamics, simulation methods for the Ising model and atomic fluids, simulation methods for quantum-mechanical problems, time-dependent Schrödinger equation. Langevin dynamics simulation. Density Functional Theory

Data Science

Python programming for data science using libraries such as Numpy, Pandas, and Scikit- learn, basics of statistics, data visualization using python libraries, machine learning for building model with data, machine learning algorithms, such as supervised learning, and reinforcement learning.

References:

1. V. Rajaraman, Computer Programming in Fortran 77, Prentice Hall
2. W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press
3. H.M. Antia, Numerical Methods for Scientists and Engineers, Hindustan Book Agency
4. Mahendra K. Verma, Practical Numerical Computing Using Python: Scientific & Engineering Applications.
5. D.W. Heermann, Computer Simulation Methods in Theoretical Physics, Springer
6. H. Gould and J. Tobochnik, An Introduction to Computer Simulation Methods, Addison- Wesley
7. J.M. Thijssen, Computational Physics, Cambridge University Press
8. Joel Grus. Data Science from Scratch
9. David Spiegelhalter, The Art of Statistics, How to learn from Data
10. Roger Pend and Elizabeth Matsui, The Art of Data Science

                

                 Fundamentals of Electronics (3 credits)

               

                  Introduction

Survey of network theorems, port-based circuit analysis, passive and active network, AC and DC bridges,

Electronic Devices

General properties of semiconductors. Schottky diode, p-n junction, Diodes, light-emitting diodes, photo-diodes, negative-resistance devices, p-n-p-n characteristics, transistors (FET, MoSFET, bipolar), CMOS.

Transistors at low and high frequencies, FET, Basic differential amplifier circuit, operational amplifier - characteristics and applications, simple analog computer, analog integrated circuits.

Digital Electronics

Logic gates, gates using CMOS, combinational and sequential digital systems, Reduction of Karnaugh map, flip-flops, types and implementation (conversion, triggering, master/slave implementation), counters (binary up down counters, synchronous counters), multi-channel analyzer, converters (ADC, DAC). Basics of VLSI.

Introduction to microprocessors (8085 and 8086) and Its architecture, data addressing modes, arithmetic and logic instruction, advanced microprocessors.

Wireless Communication electronics

Basic of RF circuits, Design and analysis of RF circuits, RF transceiver and communication system, electromagnetic transmission and signal propagation

References:

1. P. Horowitz and W. Hill, The Art of Electronics, Cambridge University Press
2. J. Millman and A. Grabel, Microelectronics, McGraw-Hill
3. J.J. Cathey, Schaum's Outline of Electronic Devices and Circuits, McGraw-Hill
4. M. Forrest, Electronic Sensor Circuits and Projects, Master Publishing Inc
5. W. Kleitz, Digital Electronics: A Practical Approach, Prentice Hall
6. J.H. Moore, C.C. Davis and M.A. Coplan, Building Scientific Apparatus, Cambridge University Press
7. Adel S. Sedra and Kenneth C. Smith, Micro-electronics circuits: Theory and Applications,

, 7^th edition, 2017.

8. Robert Sobot, Wireless Communication Electronics, , second edition, 2020

Electronics Laboratory (3 Credits)

• • Circuit analysis using Thevenin's theorem and Kirchhoff’s law.
  • Characteristics of diode, BJT, FET, FET-switch
  • Analysis of feedback circuits
  • Differential amplifier and current mirror circuits
  • Characteristics of OPAMP and Trigger circuit
  • Digital electronics
  • Analysis of RF amplifier, modulator/demodulator, oscillator circuits, RF transceiver operation
  • Microcontrollers and FPGA programming.

                   Atomic and Molecular Physics (4 credits)

Many-electron atoms and ions

Review of H and He atom, Central field approximation, Thomas-Fermi model. Wave function as Slater determinant. Self-consistent Hartree-Fock method. Corrections: correlation effects, LS and JJ coupling. Density functional theory.

Molecular quantum mechanics, Hydrogen molecular ion (numerical solution), hydrogen molecule, Heitler-London method, molecular orbital, Born-Oppenheimer approximation, Linear combination of atomic orbitals(LCAO).

Atomic and molecular spectroscopy

Fine and hyperfine structure of atoms. Isotope effect. Line width, thermal and Doppler broadening. Effect of external fields. Stark, Zeeman and Paschen-Back effects.

Microwave spectroscopy, Rotational spectra, Infrared spectroscopy, Break-down of Born- Oppenheimer approximations: the Interaction of rotations and vibrations, Vibrational and rotational spectra for diatomic molecules, role of symmetry, selection rules, term schemes, applications to electronic and vibrational problems. Raman spectroscopy, Rotational and vibrational Raman spectra, Electronic spectroscopy of atoms, Angular momentum of Many electron atoms, Electronic spectra of diatomic Molecules, electronic spectra of polyatomic molecules

Interaction of atoms with radiation

Atoms in an electromagnetic field, absorption and induced emission, spontaneous emission and line-width, Einstein A and B coefficients. Population inversion, Lasers and Masers.

Density matrix formalism, two-level atoms in a radiation field.

References:

1. B.H. Bransden and C.J. Joachain, Physics of Atoms and Molecules, Pearson
2. Colin N Banwell and Elaine M McCash, Fundamentals of Molecular Spectroscopy, TMH Publishing
3. L.D. Landau and E.M. Lifshitz, Quantum Mechanics, Pergamon Press
4. M. Karplus and R.N. Porter, Atoms and Molecules: An Introduction for Students of Physical Chemistry, W.A. Benjamin
5. P.W. Atkins and R.S. Friedman, Molecular Quantum Mechanics, Oxford

University Press

6. W.A. Harrison, Applied Quantum Mechanics, World Scientific
7. C.J. Foot, Atomic Physics, Oxford Univ Press
8. G. Woodgate, Elementary Atomic Structure, Oxford Univ Press

Nuclear and Particle Physics (4 credits)

Nuclear Physics

Rutherford scattering and the discovery of the nucleus. Scattering as probe. Kinematics of (non-)relativistic scattering. Cross-section, form factors.

Properties of nuclei: size, mass, charge, angular momentum, magnetic moment, parity, quadrupole moment. Charge and mass distribution. Mass defect, binding-energy, liquid drop model, Bethe-Weiszacker mass formula. Magic numbers, shell model, parity and magnetic moment.

Nuclear stability: alpha, beta and gamma decay. Tunnelling theory of alpha decay, Fermi theory of beta decay, selection rules in gamma decay. Parity violation.

Fission and fusion. Nuclear reaction.

Nuclear force. Deuteron, properties of nuclear potentials. Yukawa's hypothesis.

Accelerators and Detectors

Van de Graaf generator and pelletron. Linear accelerator. Cyclotron and synchrotron. Accelerator facilities in India. Medical and industrial applications on accelerators.

Particle detectors, Elementary nuclear reactor physics

Particle Physics

Discovery of elementary particles in cosmic rays. Muon, meson and strange particles. Isospin and strangeness.

Isospin, strangeness and SU(3) flavour symmetry. Introduction to group theory. Discrete

groups, parity, time reversal and charge conjugation. Continuous groups, with emphasis on SO(3), SU(2), SU(3) and Lorentz groups.

Quark hypothesis, Meson and Baryon octets. Gellmann-Nishijima formula. Discovery of J/psi, charm quark. Families of leptons and quarks. Bottom and top quarks. Colour quantum number, quarks and gluons.

Elements of gauge symmetry and fundamental forces. Weak interaction, W and Z bosons. Electroweak unification, Higgs mechanism and spontaneous symmetry breaking. Higgs particle. Gluons and strong interaction.

Neutrino oscillations. CP violation.

References:

1. B.L. Cohen, Concepts of Nuclear Physics, Tata McGraw Hill
2. W.N. Cottingham and D.A. Greenwood, An introduction to Nuclear Physics,

Cambridge University Press

3. K.S. Krane, Introductory Nuclear Physics, Wiley
4. I. Kaplan, Nuclear Physics, Addison-Wesley
5. R.R. Roy and B.P. Nigam, Nuclear Physics: Theory and Experiment, Wiley
6. B.R. Martin, Nuclear and Particle Physics, Wiley
7. A. Das and T. Ferbel, Introduction to Nuclear and Particle Physics, World Scientific
8. B. Povh, K. Rith, C. Scholtz and F. Zetsche, Particles and Nuclei, Springer
9. G.D. Coughlan and J.E. Dodd, The Ideas of Particle Physics, Cambridge University Press
10. D. Griffiths, Introduction to Elementary Particles, Wiley
11. T. De, Particle Physics: A Primer, Levant Books
12. H. Georgi, Lie Algebras in Particle Physics, Levant Books
13. A. Das and S. Okubo, Lie Groups and Lie Algebras for Physicists, Hindustan Book Agency

             Masters Dissertation-I (8 Credits)

Probability and statistics:

Repeated experiments and empirical notion of probability. Random variables. Probability density function. Examples (binomial, Poisson and normal). Covariance. Central limit theorem. Notion of statistical significance.

Scientific ethics

Ethical practice in experimental and theoretical research. Plagiarism and self-plagiarism.

Masters Dissertation

Experimental Physics II (4 credits)

Minimum 8 experiments have to be completed during the semester.

• • Electron spin resonance
  • Faraday rotation and Kerr effect
  • Study of interfacial tension and viscosity of liquid
  • Reaction kinetics by spectrometer and conductivity
  • Experiment with Raman spectrometer
  • Propagation of ultrasonic waves in liquid and solid
  • Experiment with solar cell
  • Dielectric constant of ice and ferroelectric transition of BaTiO3
  • Zeeman effect
  • Study of superconducting properties in high-Tc superconductor
  • Experiment with liquid using UV spectroscopy
  • Identification of unknown samples using the powder diffraction method.
  • Determination of elastic constants of a cubic crystal by ultrasonic velocity measurements

Masters Dissertation -II (8 credits)

Syllabus for Elective Courses

Advanced Statistical Mechanics-II (4 credits)

Phase Transitions and Critical Phenomena

Thermodynamics of phase transitions, metastable states, Van der Waals' equation of state, coexistence of phases, Landau theory, critical phenomena at second-order phase transitions, spatial and temporal fluctuations, scaling hypothesis, critical exponents,

universality classes.

Mean Field Theory

Ising model, mean-field theory, exact solution in one dimension, renormalization in one dimension.

Nonequilibrium Statistical Mechanics

Systems out of equilibrium, kinetic theory of a gas, approach to equilibrium and the H- theorem, Boltzmann equation and its application to transport problems, master equation and irreversibility, simple examples, ergodic theorem.

Brownian motion, Langevin equation, fluctuation-dissipation theorem, Einstein relation, Fokker-Planck equation.

Correlation Functions

Time correlation functions, linear response theory, Kubo formula, Onsager relations.

Coarse-grained Models

Hydrodynamics, Navier-Stokes equation for fluids, simple solutions for fluid flow, conservation laws and diffusion.

References:

1. K. Huang, Statistical Mechanics, Wiley
2. R.K. Pathria, Statistical Mechanics, Elsevier
3. E.M. Lifshitz and L.P. Pitaevskii, Physical Kinetics, Pergamon Press
4. D.A. McQuarrie, Statistical Mechanics, University Science Books
5. L.P. Kadanoff, Statistical Physics: Statistics, Dynamics and Renormalization, World Scientific
6. P.M. Chaikin and T.C. Lubensky, Principles of Condensed Matter Physics, Cambridge University Press