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M.Sc. Courses
Semester I
Semester II
PS 411 Mathematical Physics
PS 421 Quantum Mechanics II (3 credits)
(3 credits)
PS 412 Classical Mechanics
(3 credits)
PS 422 Statistical Mechanics I (3 credits)
PS 413 Quantum Mechanics
I (3 credits)
PS 423 Electromagnetic Theory (3 credits)
PS 415 Physics Laboratory I
(6 credits)
PS 427 Computational Physics (3 credits)
PS 425 Electronics (2 credits)
PS 426 Physics Laboratory (4 credits)
Semester III
Semester IV
PS 511 Condensed Matter
Physics (3 credits)
PS 521 Modern Experiments: A Survey (2
credits)
PS 512 Subatomic Physics
(3 credits)
PS 522 Project (4 credits)
(Projects will be assigned at the beginning of
Semester III.)
PS 513 Statistical Mechanics
Electives *
II (3 credits)
PS 514 Atoms and Molecules
(3 credits)
PS 523 Astrophysics, Gravitation and
Cosmology (3 credits)
PS 515 Physics Laboratory
III (6 credits)
PS 524 Quantum Field Theory (3 credits)
PS 525 Biophysics (3 credits)
PS 526 Laser Physics (3 credits)
PS 527 Advanced Condensed Matter Physics
(3 credits)
PS 528 Nonlinear Dynamics (3 credits)
*Three or more courses from the following list will be offered in Semester IV.
M.Sc.
students may also take any of the Pre-Ph.D. courses offered as elective, if recommended
by the M.Sc. Student Advisor. Every M.Sc. student is required to take three electives.
Mathematical Physics
PS 411
1. Matrices
Linear vector spaces, matrix spaces, linear operators, eigenvectors and eigenvalues,
matrix diagonalization, special matrices.
2. Group Theory
Symmetries and groups, multiplication table and representations, permutation
group, translation and rotation groups, O(N) and U(N) groups.
3. Complex Analysis
Analytic functions, Cauchy-Riemann conditions, classification of singularities,
Cauchy's theorem, Taylor and Laurent expansions, analytic continuation, residue
theorem, evaluation of definite integrals, summation of series, gamma function, zeta
function, method of steepest descent.
4. Ordinary Differential Equations and Special Functions
Linear ordinary differential equations and their singularities, series solution of
second- order equations, hypergeometric and Bessel functions, classical polynomials,
Sturm- Liouville problem, expansion in orthogonal functions.
References:
1.
2.
3.
4.
5.
6.
7.
G.B. Arfken, Mathematical Methods for Physicists.
P. Dennery and A. Krzywicki, Mathematics for Physicists.
P.K. Chattopadhyay, Mathematical Physics.
A.W. Joshi, Matrices and Tensors in Physics.
R.V. Churchill and J.W. Brown, Complex Variables and Applications.
P.M. Morse and H. Feshbach, Methods of Theoretical Physics (Volume I &
II).
M.R. Spiegel, Complex Variables.
Top
Classical Mechanics
PS 412
1. Lagrangian and Hamiltonian Formulations of Mechanics
Calculus of variations, Hamilton's principle of least action, Lagrange's equations of
motion, conservation laws, systems with a single degree of freedom, rigid body
dynamics, symmetrical top, Hamilton's equations of motion, phase plots, fixed points
and their stabilities.
2. Two-Body Central Force Problem
Equation of motion and first integrals, classification of orbits, Kepler problem,
scattering in central force field.
3. Small Oscillations
Linearization of equations of motion, free vibrations and normal coordinates, forced
oscillations.
4. Special Theory of Relativity
Lorentz transformation, relativistic kinematics and dynamics, E=mc2.
5. Hamiltonian Mechanics and Chaos
Canonical transformations, Poisson brackets, Hamilton-Jacobi theory, action-angle
variables, perturbation theory, integrable systems, introduction to chaotic dynamics.
References:
1.
2.
3.
4.
5.
6.
H. Goldstein, Classical Mechanics.
L.D. Landau and E.M. Lifshitz, Mechanics.
I.C. Percival and D. Richards, Introduction to Dynamics.
J.V. Jose and E.J. Saletan, Classical Dynamics: A Contemporary Approach.
E.T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid
Bodies.
N.C. Rana and P.S. Joag, Classical Mechanics.
Top
Quantum Mechanics I
PS 413
1. Introduction
Empirical basis, wave-particle duality, electron diffraction, notion of state vector and
its probability interpretation.
2. Structure of Quantum Mechanics
Operators and observables, significance of eigenfunctions and eigenvalues,
commutation relations, uncertainty principle, measurement in quantum theory.
3. Quantum Dynamics
Time-dependent Schrödinger equation, stationary states and their significance, timeindependent Schrödinger equation.
4. One-dimensional Schrödinger Equation
Free-particle solution, wave packets, particle in a square well potential, transmission
through a potential barrier, simple harmonic oscillator by wave equation and
operator methods, charged particle in a uniform magnetic field, coherent states.
5. Spherically Symmetric Potentials
Separation of variables in spherical polar coordinates, orbital angular momentum,
parity, spherical harmonics, free particle in spherical polar coordinates, square well
potential, hydrogen atom.
References:
1.
2.
3.
4.
5.
6.
C. Cohen-Tannoudji, B. Diu and F. Laloe, Quantum Mechanics (Volume I).
L.I. Schiff, Quantum Mechanics.
E. Merzbacher, Quantum Mechanics.
R.P. Feynman, Feynman Lectures on Physics (Volume 3).
A. Messiah, Quantum Mechanics (Volume I).
R. Shankar, Principles of Quantum Mechanics.
Top
Physics Laboratory I
PS 415
1.
G.M.
Counter.
2.
Experiments
with
microwaves.
3. Electrical resistance of a superconductor, metal and a semiconductor.
4.
Work
function
of
Tungsten,
Richardson's
equation.
5.
Hall
effect.
6.
Thermal
conductivity
of
Teflon.
7.
Susceptibility
of
Gadolinium.
8.
Transmission
line,
propagation
of
mechanical
and
EM
waves.
9.
Dielectric
constant
of
ice.
10.
Elastic
properties
of
a
solid
using
piezoelectric
oscillator.
11.
Measurement
of
e/m
by
Thomson
effect.
12.
Measurement
of
Planck's
constant
by
photoelectric
effect.
13.
Michelson
interferometer.
Note: Each student is required to perform at least 8 of the above experiments.
Top
Quantum Mechanics II
PS 421
1. Symmetry in Quantum Mechanics
Symmetry operations and unitary transformations, conservation principles, space
and time translations, rotation, space inversion and time reversal, symmetry and
degeneracy.
2. Angular Momentum
Rotation operators, angular momentum algebra, eigenvalues of J2 and Jz, spinors and
Pauli matrices, addition of angular momenta.
3. Identical Particles
Indistinguishability, symmetric and antisymmetric wave functions, incorporation of
spin, Slater determinants, Pauli exclusion principle.
4. Time-independent Approximation Methods
Non-degenerate perturbation theory, degenerate case, Stark effect, Zeeman effect
and other examples, variational methods, WKB method, tunnelling.
5. Time-dependent Problems
Schrödinger and Heisenberg picture, time-dependent perturbation theory, transition
probability calculations, golden rule, adiabatic approximation, sudden approximation,
beta decay as an example.
6. Scattering Theory
Differential cross-section, scattering of a wave packet, integral equation for the
scattering amplitude, Born approximation, method of partial waves, low energy
scattering and bound states, resonance scattering.
References:
Same as in Quantum Mechanics I plus
1. C. Cohen-Tannoudji, B. Diu and F. Laloe, Quantum Mechanics (Volume II).
2. A. Messiah, Quantum Mechanics (Volume II).
3. S. Flügge, Practical Quantum Mechanics.
4. J.J. Sakurai, Modern Quantum Mechanics.
5. K. Gottfried, Quantum Mechanics.
Top
Statistical Mechanics I
PS 422
1. Elementary Probability Theory
Binomial, Poisson and Gaussian distributions, central limit theorem.
2. 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.
3. Formalism of Equilibrium Statistical Mechanics
Concept of phase space, Liouville's theorem, basic postulates of statistical
mechanics, ensembles: microcanonical, canonical, grand canonical, and isobaric,
connection 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.
4. Quantum Statistics
Fermi-Dirac and Bose-Einstein statistics. Applications of the formalism to:
(a) 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.
(b) Ideal Fermi gas, properties of simple metals, Pauli paramagnetism, electronic
specific heat, white dwarf stars.
References:
1.
2.
3.
4.
5.
F. Reif, Fundamentals of Statistical and Thermal Physics.
K. Huang, Statistical Mechanics.
R.K. Pathria, Statistical Mechanics.
D.A. McQuarrie, Statistical Mechanics.
S.K. Ma, Statistical Mechanics.
Top
Electromagnetic Theory
PS 423
1. Electrostatics
Differential equation for electric field, Poisson and Laplace equations, formal solution
for potential with Green's functions, boundary value problems, examples of image
method and Green's function method, solutions of Laplace equation in cylindrical and
spherical coordinates by orthogonal functions, dielectrics, polarization of a medium,
electrostatic energy.
2. Magnetostatics
Biot-Savart law, differential equation for static magnetic field, vector potential,
magnetic field from localized current distributions, examples of magnetostatic
problems, Faraday's law of induction, magnetic energy of steady current
distributions.
3. Maxwell's Equations
Displacement current, Maxwell's equations, vector and scalar potentials, gauge
symmetry, Coulomb and Lorentz gauges, electromagnetic energy and momentum,
conservation laws, inhomogeneous wave equation and Green's function solution.
4. 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.
5. Radiation
Field of a localized oscillating source, fields and radiation in dipole and quadrupole
approximations, antenna, radiation by moving charges, Lienard-Wiechert potentials,
total power radiated by an accelerated charge, Lorentz formula.
6. Covariant Formulation of Electrodynamics
Four-vectors relevant to electrodynamics, electromagnetic field tensor and Maxwell's
equations, transformation of fields, fields of uniformly moving particles.
7. Concepts of Plasma Physics
Formation of plasma, Debye theory of screening, plasma oscillations, motion of
charges in electromagnetic fields, magneto-plasma, plasma confinement,
hydromagnetic waves.
References:
1. J.D. Jackson, Classical Electrodynamics.
2. D.J. Griffiths, Introduction to Electrodynamics.
3. J.R. Reitz, F.J. Milford and R.W. Christy, Foundations of Electromagnetic
Theory.
4. W.K.H. Panofsky and M. Phillips, Classical Electricity and Magnetism.
5. F.F. Chen, Introduction to Plasma Physics and Controlled Fusion.
Top
Computational Physics
PS 427
1.
Overview of computer organization, hardware, software, scientific programming in
FORTRAN and/or C, C++.
2. Numerical Techniques
Sorting, interpolation, extrapolation, regression, 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, fast Fourier
transforms.
3. Simulation Techniques
Monte Carlo methods, molecular dynamics, simulation methods for the Ising model
and atomic fluids, simulation methods for quantum-mechanical problems, timedependent Schrödinger equation, discussion of selected problems in percolation,
cellular automata, nonlinear dynamics, traffic problems, diffusion-limited
aggregation, celestial mechanics, etc.
4. Parallel Computation
Introduction to parallel computation.
References:
1. V. Rajaraman, Computer Programming in Fortran 77.
2. W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling, Numerical
Recipes in FORTRAN 77: The Art of Scientific Computing. (Similar volumes in C,
C++.)
3. H.M. Antia, Numerical Methods for Scientists and Engineers.
4. D.W. Heermann, Computer Simulation Methods in Theoretical Physics.
5. H. Gould and J. Tobochnik, An Introduction to Computer Simulation Methods.
6. J.M. Thijssen, Computational Physics.
Top
Electronics
PS 425
1. Introduction
Survey of network theorems and network analysis, AC and DC bridges, transistors at
low and high frequencies, FET.
2. Electronic Devices
Diodes, light-emitting diodes, photo-diodes, negative-resistance devices, p-n-p-n
characteristics, transistors (FET, MoSFET, bipolar).
Basic differential amplifier circuit, operational amplifier characteristics and
applications, simple analog computer, analog integrated circuits.
3. Digital Electronics
Gates, combinational and sequential digital systems, flip-flops, counters, multichannel analyzer.
4. Electronic Instruments
Power supplies, oscillators, digital oscilloscopes, counters, phase-sensitive detectors,
introduction to micro-processors.
References:
1.
2.
3.
4.
5.
6.
P. Horowitz and W. Hill, The Art of Electronics.
J. Millman and A. Grabel, Microelectronics.
J.J. Cathey, Schaum's Outline of Electronic Devices and Circuits.
M. Forrest, Electronic Sensor Circuits and Projects.
W. Kleitz, Digital Electronics: A Practical Approach.
J.H. Moore, C.C. Davis and M.A. Coplan, Building Scientific Apparatus.
Top
Physics Laboratory II
PS 426
1. To trace I-V characteristic curves of diodes and transistors on a CRO, and learn
their uses in electronic circuits.
2. Negative feedback and amplifier characteristics.
3. Uses of differential amplifier and op amps in linear circuits.
4. Design of simple logic gates using transistors.
5. To study transfer characteristics of a regenerative comparator, to design a time
marker, sample, hold and multiplier circuits, to design a sweep generator using a
Schmitt trigger.
6. AD/DA converter/GPIB interfacing.
7. Circuit simulation using SPICE.
8. Microwave generators.
9. Experiments with timers/pulse generators etc.
10. Digital electronics.
11. Microprocessor-based experiment.
12. Project (design of audio amplifier/digital clock/regulated power supply).
Note: Each student is required to perform at least 8 of the above experiments.
Top
Condensed Matter Physics
PS 511
1. 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.
2. 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.
3. Classification of Solids
Band classifications, covalent, molecular and ionic crystals, nature of bonding,
cohesive energies, hydrogen bonding.
4. Electron States in Crystals
Periodic potential and Bloch's theorem, weak potential approximation, energy gaps,
Fermi surface and Brillouin zones, Harrison construction, level density.
5. Electron Dynamics
Wave packets of Bloch electrons, semi-classical equations of motion, motion in static
electric and magnetic fields, theory of holes.
6. Lattice Dynamics
Failure of the static lattice model, harmonic approximation, vibrations of a onedimensional 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.
7. Semiconductors
General properties and band structure, carrier statistics, impurities, intrinsic and
extrinsic semiconductors, p-n junctions, equilibrium fields and densities in junctions,
drift and diffusion currents.
8. Magnetism
Diamagnetism, paramagnetism of insulators and metals, ferromagnetism, CurieWeiss law, introduction to other types of magnetic order.
9. Superconductors
Phenomenology, review of basic properties, thermodynamics of superconductors,
London's equation and Meissner effect, Type-I and Type-II superconductors.
References:
1.
2.
3.
4.
5.
6.
C. Kittel, Introduction to Solid State Physics.
N.W. Ashcroft and N.D. Mermin, Solid State Physics.
J.M. Ziman, Principles of the Theory of Solids.
A.J. Dekker, Solid State Physics.
G. Burns, Solid State Physics.
M.P. Marder, Condensed Matter Physics.
Top
Subatomic Physics
PS 512
1. Nuclear Physics
Discovery of the nucleus, Rutherford formula, form factors, nuclear size,
characteristics of nuclei, angular momentum, magnetic moment, parity, quadrupole
moment.
Mass defect, binding-energy statistics, Weiszacker mass formula, nuclear stability,
Alpha-decay, tunnelling theory, fission, liquid drop model.
Nuclear forces, nucleon-nucleon scattering, deuteron problem, properties of nuclear
potentials, Yukawa's hypothesis.
Magic numbers, shell model, calculation of nuclear parameters, basic ideas of nuclear
reactions.
2. Particle Physics
Relativistic quantum theory, Dirac's equation and its relativistic covariance, intrinsic
spin and magnetic moment, negative energy solution and the concept of antiparticle.
Accelerators and detectors, discovery of mesons and strange particles, isospin and
internal symmetries, neutrino oscillations, quarks, parity violation, K-mesons, CP
violation.
3. Weak Interactions
Fermi's theory of beta-decay, basic ideas of gauge symmetry, spontaneous
symmetry breaking, elements of electro-weak theory, discovery of W-bosons.
4. Strong Interactions
Deep inelastic scattering, scaling concepts, quark model interpretation, colour
quantum number, asymptotic freedom, quark confinement, standard model.
References:
1.
2.
3.
4.
5.
6.
7.
G.D. Coughlan and J.E. Dodd, The Ideas of Particle Physics.
D. Griffiths, Introduction to Elementary Particles.
D.H. Perkins, Introduction to High Energy Physics.
I. Kaplan, Nuclear Physics.
R.R. Roy and B.P. Nigam, Nuclear Physics.
M.A. Preston and R.K. Bhaduri, Structure of the Nucleus.
M.G. Bowler, Nuclear Physics.
Top
Statistical Mechanics II
PS 513
1. 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.
2. Ising Model
Ising model, mean-field theory, exact solution in one dimension, renormalization in
one dimension.
3. Nonequilibrium Systems
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.
4. Correlation Functions
Time correlation functions, linear response theory, Kubo formula, Onsager relations.
5. Coarse-grained Models
Hydrodynamics, Navier-Stokes equation for fluids, simple solutions for fluid flow,
conservation laws and diffusion.
References:
1.
2.
3.
4.
5.
6.
K. Huang, Statistical Mechanics.
R.K. Pathria, Statistical Mechanics.
E.M. Lifshitz and L.P. Pitaevskii, Physical Kinetics.
D.A. McQuarrie, Statistical Mechanics.
L.P. Kadanoff, Statistical Physics: Statistics, Dynamics and Renormalization.
P.M. Chaikin and T.C. Lubensky, Principles of Condensed Matter Physics.
Top
Atoms and Molecules
PS 514
1. Many-electron Atoms
Review of He atom, ground state and first excited state, quantum virial theorem,
Thomas-Fermi method, determinantal wave function, Hartree and Hartree-Fock
method, periodic table and atomic properties: ionization potential, electron affinity,
Hund's rule.
2. Molecular Quantum Mechanics
Hydrogen molecular ion, hydrogen molecule, Heitler-London method, molecular
orbital, Born-Oppenheimer approximation, bonding, directed valence.
3. Atomic and Molecular Spectroscopy
Fine and hyperfine structure of atoms, electronic, vibrational and rotational spectra
for diatomic molecules, role of symmetry, selection rules, term schemes, applications
to electronic and vibrational problems.
4. Second Quantization
Basis sets for identical-particle systems, number space representation, creation and
annihilation operators, representation of dynamical operators and the Hamiltonian,
simple applications.
5.
Interaction of Atoms with Radiation
Atoms in an electromagnetic field, absorption and induced emission, spontaneous
emission and line-width, Einstein A and B coefficients, density matrix formalism, twolevel atoms in a radiation field.
References:
1.
2.
3.
4.
5.
6.
7.
8.
I.N. Levine, Quantum Chemistry.
R. McWeeny, Coulson's Valence.
L.D. Landau and E.M. Lifshitz, Quantum Mechanics.
M. Karplus and R.N. Porter, Atoms and Molecules: An Introduction for
Students of Physical Chemistry.
P.W. Atkins and R.S. Friedman, Molecular Quantum Mechanics.
M. Tinkham, Group Theory and Quantum Mechanics.
L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems.
W.A. Harrison, Applied Quantum Mechanics.
Top
Physics Laboratory III
PS 515
1. Electron-spin resonance.
2. Faraday rotation/Kerr effect.
3. Interfacial tension and Phase separation kinetics.
4. Reaction kinetics by spectrophotometer and conductivity.
5. Study of color centres by spectrophotometer.
6. Alpha, Beta and Gamma ray spectrometer.
7. Mössbauer spectrometer.
8. Sizing nano-structures (UV-VIS spectroscopy).
9. Magneto-resistance and its field dependence.
10. X-ray diffraction.
11. Compton scattering.
12. Adiabatic compressibility.
13. Solid-liquid phase diagram for a mixture.
Note: Each student is required to perform at least 8 of the above experiments.
Top
Modern Experiments: A Survey
PS 521
Note: This course will familiarize students with some landmark experiments in
physics through the original papers which reported these experiments. A
representative list is as follows:
1. Mössbauer effect.
2. Pound-Rebka experiment to measure gravitational red shift.
3. Parity violation experiment of Wu et al.
4. Superfluidity of He3.
5. Cosmic microwave background radiation.
6. Helicity of the neutrino.
7. Quantum Hall effect - integral and fractional.
8. Laser cooling of atoms.
9. Ion traps.
10. Bose-Einstein condensation.
11. Josephson tunneling.
12. Atomic clocks.
13. Interferometry for gravitational waves.
14. Quantum entanglement experiments: Teleportation experiment, Aspect's
experiment on Bell's inequality.
15. Inelastic neutron scattering.
16. CP violation.
17. J/Psi resonance
18. Verification of predictions of general theory of relativity by binary-pulsar and
other experiments.
19 Precision measurements of magnetic moment of electron.
20. Libchaber experiment on period-doubling route to chaos.
21. Anfinson's experiment on protein folding.
22. Scanning tunnelling microscope.
Top
Astrophysics, Gravitation and Cosmology
PS 523
1. Physics of the Universe
Astronomical observations and instruments, stellar spectra and structure, stellar
evolution, nucleosynthesis and formation of elements, evolution and origin of
galaxies, quasars, pulsars, expansion of the universe, big-bang model, CMBR,
anisotropy.
2. General Relativity
Review of special theory of relativity, four-vector formulation of Lorentz
transformation, covariant formulation of physical laws, introduction to general
relativity, principle of equivalence, tensor analysis and Riemannian geometry,
curvature and stress-energy tensors, gravitational field equations, geodesics and
particle trajectories, Schwarschild solution, Kerr solution, gravitational waves,
relativistic stellar structure, TOV equation, basic cosmology.
References:
1.
2.
3.
4.
5.
K.D. Abhyankar, Astrophysics: Stars and Galaxies.
J.V. Narlikar, An Introduction to Cosmology.
C.W. Misner, K. Thorne, J.A. Wheeler, Gravitation.
R. Adler, M. Bazin and M. Schiffer, Introduction to General Relativity.
T. Padmanabhan, Cosmology and Astrophysics through Problems.
Top
Quantum Field Theory
PS 524
1. String waves, water waves, etc. as examples of classical fields, Lagrangian and
Hamiltonian formulation of a vibrating string fixed at both ends in analogy with
Newtonian particles.
2. Relativistic kinematics, relativistic waves, Klein-Gordon (KG) equation as a
relativistic wave equation, treatment of the KG equation as a classical wave
equation: its Lagrangian and Hamiltonian, Noether's theorem and derivation of
energy-momentum and angular momentum tensors as consequence of Poincaré
symmetry, internal symmetry and the associated conserved current.
3. Canonical quantization of the KG field, solution of KG theory in Schrödinger and
Heisenberg pictures, expansion in terms of creation and annihilation operators,
definition of the vacuum and N-particle eigenstates of the Hamiltonian, vacuum
expectation values, propagators, spin and statistics of the KG quantum.
4. Review of Dirac equation and its quantization, use of anti-commutators, creation
and destruction operators of particles and antiparticles, Dirac propagator, energy,
momentum and angular momentum, spin and statistics of Dirac quanta.
5. Review of free Maxwell's equations, Lagrangian, gauge transformation and gauge
fixing, Hamiltonian, quantization in terms of transverse delta functions, expansion
in terms of creation operators, spin, statistics and propagator of the photon.
6. Introduction to interacting quantum fields.
References:
1.
2.
3.
4.
5.
C. Itzykson and J.-B. Zuber, Quantum Field Theory.
J.D. Bjorken and S.D. Drell, Relativistic Quantum Fields.
L. Ryder, Quantum Field Theory.
V.B. Berestetskii, E.M. Lifshitz and L.P. Pitaevskii, Quantum
Electrodynamics.
M.E. Peskin and D.V. Schroeder, An Introduction to Quantum Field Theory.
Top
Biophysics
PS 525
1. Introduction
Evolution of biosphere, aerobic and anaerobic concepts, models of evolution of living
organisms.
2. Physics of Polymers
Nomenclature, definitions of molecular weights, polydispersity, degree of
polymerization, possible geometrical shapes, chirality in biomolecules, structure of
water and ice, hydrogen bond and hydrophobocity.
3. Static Properties
Random flight model, freely-rotating chain model, scaling relations, concept of
various radii (i.e., radius of gyration, hydrodynamic radius, end-to-end length), endto-end length distributions, concept of segments and Kuhn segment length, excluded
volume interactions and chain swelling, Gaussian coil, concept of theta and good
solvents with examples, importance of second virial coefficient.
4. Polyelectrolytes
Concepts and examples, Debye-Huckel theory, screening length in electrostatic
interactions.
5. Transport Properties
(a) Diffusion: Irreversible thermodynamics, Gibbs-Duhem equation,
phenomenological forces and fluxes, osmotic pressure and second virial coefficient,
generalized diffusion equation, Stokes-Einstein relation, diffusion in three-component
systems, balance of thermodynamic and hydrodynamic forces, concentration
dependence, Smoluchowski equation and reduction to Fokker-Planck equation,
concept of impermeable and free-draining chains.
(b) Viscosity and Sedimentation: Einstein relation, intrinsic viscosity of polymer
chains, Huggins equation of viscosity, scaling relations, Kirkwood-Riseman theory,
irreversible thermodynamics and sedimentation, sedimentation equation,
concentration dependence.
6. Physics of Proteins
Nomenclature and structure of amino acids, conformations of polypeptide chains,
primary, secondary and higher-order structures, Ramachandran map, peptide bond
and its consequences, pH-pK balance, protein polymerization models, helix-coil
transitions in thermodynamic and partition function approach, coil-globule
transitions, protein folding, protein denaturation models, binding isotherms, binding
equilibrium, Hill equation and Scatchard plot.
7. Physics of Enzymes
Chemical kinetics and catalysis, kinetics of simple enzymatic reactions, enzymesubstrate interactions, cooperative properties.
8. Physics of Nucleic Acids
Structure of nucleic acids, special features and properties, DNA and RNA, WatsonCrick picture and duplex stabilization model, thermodynamics of melting and kinetics
of denaturation of duplex, loops and cyclization of DNA, ligand interactions, genetic
code and protein biosynthesis, DNA replication.
9. Experimental Techniques
Measurement concepts and error analysis, light and neutron scattering, X-ray
diffraction, UV spectroscopy, CD and ORD, electrophoresis, viscometry and rheology,
DSC and dielectric relaxation studies.
10. Recent Topics in Bio-Nanophysics
References:
1. M.V. Volkenstein, General Biophysics.
2. C.R. Cantor and P.R. Schimmel, Biophysical Chemistry Part III: The
Behavior of Biological Macromolecules.
3. C. Tanford, Physical Chemistry of Macromolecules.
4. S.F. Sun, Physical Chemistry of Macromolecules: Basic Principles and Issues.
Top
Laser Physics
PS 526
1. Introduction
Masers versus lasers, components of a laser system, amplification by population
inversion, oscillation condition, types of lasers: solid-state (ruby, Nd:YAG,
semiconductor), gas (He-Ne, CO2 excimer), liquid (organic dye) lasers.
2. Atom-Field Interactions
Lorenz theory, Einstein's rate equations, applications to laser transitions with
pumping, two, three and four-level schemes, threshold pumping and inversion.
3. Optical Resonators
Closed versus open cavities, modes of a symmetric confocal optical resonator,
stability, quality factor.
4. Semi-classical Laser Theory
Density matrix for a two-level atom, Lamb equation for the classical field, threshold
condition, disorder-order phase transition analogy.
5. Coherence
Concepts of coherence and correlation functions, coherent states of the
electromagnetic field, minimum uncertainty states, unit degree of coherence, Poisson
photon statistics.
6. Pulsed Operation of Lasers
Q-switching, electro-optic and acousto-optic modulation, saturable absorbers, modelocking.
7. Applications of Lasers
Introduction to atom optics, Doppler cooling of atoms, introduction to nonlinear
optics: self-(de) focusing, second-harmonic generation (phase-matching conditions).
References:
1.
2.
3.
4.
5.
6.
7.
8.
K. Thyagarajan and A.K. Ghatak, Lasers: Theory and Applications.
A.K. Ghatak and K. Thyagarajan, Optical Electronics.
W. Demtroeder, Laser Spectroscopy.
B.B. Laud, Lasers and Nonlinear Optics.
M. Sargent III, M.O. Scully and W.E. Lamb, Jr., Laser Physics.
M.O. Scully and M.S. Zubairy, Quantum Optics.
P. Meystre and M. Sargent III, Elements of Quantum Optics.
L. Mandel and E. Wolf, Optical Coherence and Quantum Optics.
Top
Advanced Condensed Matter Physics
PS 527
1. Dielectric Properties of Solids
Dielectric constant of metal and insulator using phenomenological theory (Maxwell's
equations), polarization and ferroelectrics, inter-band transitions, Kramers-Kronig
relations, polarons, excitons, optical properties of metals and insulators.
2. Transport Properties of Solids
Boltzmann transport equation, resistivity of metals and semiconductors,
thermoelectric phenomena, Onsager coefficients.
3. Many-electron Systems
Sommerfeld expansion, Hartree-Fock approximation, exchange interactions, concept
of quasi-particles, introduction to Fermi liquid theory, screening, plasmons.
4. Introduction to Strongly Correlated Systems
Narrow band solids, Wannier orbitals and tight-binding method, Mott insulator,
electronic and magnetic properties of oxides, introduction to Hubbard model.
5. Magnetism
Magnetic interactions, Heitler-London method, exchange and superexchange,
magnetic moments and crystal-field effects, ferromagnetism, spin-wave excitations
and thermodynamics, antiferromagnetism.
6. Superconductivity
Basic phenomena, London equations, Cooper pairs, coherence, Ginzburg-Landau
theory, BCS theory, Josephson effect, SQUID, excitations and energy gap, magnetic
properties of type-I and type-II superconductors, flux lattice, introduction to hightemperature superconductors.
References:
1.
2.
3.
4.
5.
6.
N.W. Ashcroft and N.D. Mermin, Solid State Physics.
D. Pines, Elementary Excitations in Solids.
S. Raimes, The Wave Mechanics of Electrons in Metals.
P. Fazekas, Lecture Notes on Electron Correlation and Magnetism.
M. Tinkham, Introduction to Superconductivity.
M. Marder, Condensed Matter Physics.
Top
Nonlinear Dynamics
PS 528
1. Introduction to Dynamical Systems
Physics of nonlinear systems, dynamical equations and constants of motion, phase
space, fixed points, stability analysis, bifurcations and their classification, Poincaré
section and iterative maps.
2. Dissipative Systems
One-dimensional noninvertible maps, simple and strange attractors, iterative maps,
period-doubling and universality, intermittency, invariant measure, Lyapunov
exponents, higher-dimensional systems, Hénon map, Lorenz equations, fractal
geometry, generalized dimensions, examples of fractals.
3. Hamiltonian Systems
Integrability, Liouville's theorem, action-angle variables, introduction to perturbation
techniques, KAM theorem, area-preserving maps, concepts of chaos and
stochasticity.
4. Advanced Topics
Selections from quantum chaos, cellular automata and coupled map lattices, pattern
formation, solitons and completely integrable systems, turbulence.
References:
1.
2.
3.
4.
E. Ott, Chaos in Dynamical Systems.
E.A. Jackson, Perspectives of Nonlinear Dynamics (Volumes 1 and 2).
A.J. Lichtenberg and M.A. Lieberman, Regular and Stochastic Motion.
A.M. Ozorio de Almeida, Hamiltonian Systems: Chaos and Quantization.
5. M. Tabor, Chaos and Integrability in Nonlinear Dynamics.
6. M. Lakshmanan and S. Rajasekar, Nonlinear Dynamics: Integrability,
Chaos and Patterns.
7. H.J. Stockmann, Quantum Chaos: An Introduction.