| PHY F111 |
Mechanics, Oscillations and Waves |
3 0 3 |
|
Conservation Principles, Rotational Dynamics, Oscillations, Wave Motion, Reflection and Refraction, Interference, Diffraction, Polarisation. |
| PHY F211 |
Classical Mechanics |
3 0 3 |
|
Review of Newtonian mechanics, constraints and generalized coordinates, Lagrange’s equation of motion, calculus of variationand principle of least action, central force motion, kinematicsof rigid body motion, rigid body equations of motion, heavy symmetrical top, Hamilton’s equations of motion, canonical transformations. |
| PHY F212 |
Electromagnetic Theory I |
3 0 3 |
|
Review of mathematics - scalar and vector fields, calculus of scalar and vector fields in Cartesian and curvilinear coordinates, Dirac delta function; Electrostatics - electric field, divergence & curl of electric field, electric potential, work and energy in electrostatics, conductors, electric dipole; Electrostatics in Matter - polarization and field of a polarized object, electric displacement, linear dielectrics; Magnetostatics - Lorentz force law, Biot-Savart law, divergence & curl of magnetic field, magnetic vector potential, magnetic dipole; Magnetostatics in matter - magnetization and field of a magnetized object, the H-field, linear & non-linear magnetic media; Electrodynamics - electromotive force, electromagnetic induction, Maxwell's equations in free space, planewave solutions of Maxwell’s equations in free space. |
| PHY F213 |
Optics |
3 0 3 |
|
Geometrical optics - light as rays, Fermat’s principle, matrix methods in ray tracing; scalar wave theory of light, spatial and temporal coherence, theory of diffraction - Fresnel & Fraunhoffer diffraction, diffraction at rectangular and circular aperture, diffraction around opaque objects; crystal optics – electromagnetic wave propagation in anisotropic media, birefringence, e-m waves in nonlinear media, elements of nonlinear optics; scattering of light – Thomson and Rayleigh scattering; elements of modern optics - lasers and applications, holography, fiber optics, Fourier optics. |
| PHY F215 |
Introduction to Astronomy and Astrophysics |
3 0 3 |
|
Introduction and scope, telescopes, distance and size measurements of astronomical objects, celestial mechanics, the Sun, planets, planet formation, interstellar medium, star formation, stellar structure, stellar evolution, star clusters - open clusters, globular clusters, the Milky-Way galaxy, nature of galaxies, normal and active galaxies, Newtonian cosmology, cosmic microwave background radiation, the early universe. |
| PHY F241 |
Electromagnetic Theory II |
3 1 4 |
|
Maxwell's equations in matter, boundary conditions on electric and magnetic fields; energy of e-m fields and Poynting’s theorem, linear momentum and angular momentum of e-m fields, Maxwell's stress tensor; electromagnetic waves in dielectric media – reflection, refraction and transmission at interfaces; wave propagation in metals – absorption and dispersion; guided waves; potential formulation of e-m fields, retarded potentials & Jefimenko's equations, Lienard-Weichert potentials and fields of a moving point charge; dipole radiation & radiation due to point charges; special theory of relativity, relativistic mechanics, relativistic electrodynamics. |
| PHY F242 |
Quantum Mechanics I. |
3 0 3 |
|
Origin of the quantum theory - black body radiation, photoelectric effect, Compton scattering, electron diffraction, Bohr model of hydrogen atom, Frank-Hertz experiment, Bohr-Sommerfeld quantization condition; notion of wave function, statistical interpretation of the wave function, issues of normalization, the Heisenberg uncertainty relation; Schrodinger equation, stationary states and time independent Schrodinger equation, energy eigenvalues and eigenfunctions, one-dimensional problems – potential wells, potential barriers, the harmonic oscillator; Hilbert space formalism – state vectors, Dirac’s bra-ket notation, observables as Hermitian operators, eigenvalues and eigenstates of Hermitian operators, the measurement postulate. |
| PHY F243 |
Mathematical Methods of Physics |
3 0 3 |
|
Tensor analysis in Cartesian and curvilinear coordinates; linear vector spaces, linear transformations and theory of matrices; functions of a complex variable, contour integration and applications; elements of calculus of variation; series solution of ordinary differential equations, special functions, Sturm-Liouville theory; Fourier integral; partial differential equations of physics, solution of partial differential equations by separation of variables method, the Green function method. |
| PHY F311 |
Quantum Mechanics 2 |
3 0 3 |
|
Hilbert space formalism (continued from QM-I) - operators and their matrix representations, change of basis, position and momentum representations, commuting and non-commuting observables, the generalized uncertainty relation; the time evolution operator and Schrodinger equation, Schrodinger and Heisenberg picture, simple harmonic oscillator using operator method; angular momentum operators and their commutation relations, eigenvalues and eigenvectors of angular momentum, spherically symmetric potentials, the hydrogen atom; time independent perturbation theory, WKB approximation, variational method; time dependent perturbation theory, interaction of atom with classical radiation field; identical particles. |
| PHY F312 |
Statistical Mechanics |
3 0 3 |
|
Review of Thermodynamics - First and the second law of thermodynamics, reversible and irreversible processes, entropy, absolute temperature, thermodynamic potentials ; Statistical description of macroscopic systems - micro and macro states, phase space distribution, Liouville theorem, microcanonical ensemble, statistical definition of temperature, pressure and entropy; Canonical ensembles, probability distribution in canonical ensemble, partition function and calculation of thermodynamic quantities, equipartition and virial theorems, Maxwell velocity distribution, paramgnetism, harmonic oscillators, polyatomic molecules; Grand canonical ensembles - probability distribution in grand canonical ensemble, grand partition function, calculation of thermodynamic quantities; Quantum statistics - indistinguishable particles, Bose-Einstein and Fermi-Dirac distribution, classical limit, photon statistics, Planck distribution; Ideal Fermi gas - equation of state of ideal Fermi gas, free electron gas in metals, Pauli paramagnetism, Landau diamagnetism, statistical equilibrium of white dwarf stars; Ideal Bose Gas - equation of state, Bose-Einstein condensation. |
| PHY F313 |
Computational Physics |
3 0 3 |
|
Review of programming language - C/C++, python, Matlab and Mathematica; Functions and roots - Newton-Raphson method, rate of convergence, system of algebraic equations; Numerical integration - Romberg integration, Gaussian quadrature; Ordinary differential equations - Euler Method, Runge-Kutta method, predictor- corrector method, system of equations; Partial differential equations - boundary value problems, finite difference method, finite element method; discrete and fast Fourier transform; Eigen- value problems; Monte-Carlo method - random numbers, sampling rules, metropolis algorithm. |
| PHY F341 |
Solid State Physics |
3 0 3 |
|
Crystal structure - direct and reciprocal lattice, Brillouin zone, Xray diffraction and crystal structure; free electron theory of metals; periodic potential and band theory of solids, the tight-binding approximation; lattice vibration and thermal properties; semiconductors - energy band gap in semiconductors, carrier density of intrinsic and extrinsic semiconductors, the p-n junction; magnetism - paramagnetism and diamagnetism, spontaneous magnetism, magnetic ordering; super conductivity-basic properties, the London equation, elements of BCS theory. |
| PHY F341 |
Atomic and Molecular Physics |
3 0 3 |
|
Interaction of electromagnetic field with atoms - transition rates, dipole approximation, Einstein coefficients, selection rules and spectrum of one electron atom, line intensities and shapes, line widths and lifetimes; one electron atoms - fine and hyperfine structure, interaction with external electric and magnetic fields; two electron atoms - para and ortho states, level scheme, ground and exited states of two electron atoms; many electron atoms - central field approximation, Thomas –Fermi model, Hartree- Fock method, L-S coupling and j-j coupling; Molecular structure - Born-Oppenheimer approximation, rotation and vibration of diatomic and polyatomic molecules, electronic structure and spin, rotational-vibrational and electronic spectra of diatomic molecules, nuclear spin. |
| PHY F343 |
Nuclear and Particle Physics |
3 0 3 |
|
Bethe-Weizsacker mass formula, nuclear size, mirror nuclei, electric multipole moments, Spherically and axially symmetric charge distribution, electric quadrupole moment, nuclear magnetic moment, nuclear decay, alpha and beta decay processes, nuclear fission, Bohr-Wheeler theory, two-body problem, deuteron wave function with central and non-central potential, electric quadrupole moment & magnetic moment, exchange forces, low energy nucleon-nucleon scattering, scattering length, effective range theory, spin dependence of n-p scattering, magic numbers, independent particle model, collective model. Mesons and baryons, antiparticles, neutrinos, strange particles, eightfold way, quark model, intermediate vector bosons, four fundamental forces, basic vertices and charactesitics of quantum electrodynamics, quantum flavordyamics and quantum chromo dynamics, decays and conservations laws, basic ideas of standard model of particle physics, qualitative discussion of current issues in particle physics. |
| PHY F345 |
Quantum Mechanics for Engineers |
3 0 3 |
|
Wave particle duality, Schrödinger wave equation, probability and current densities, position and momentum operators and state space, expectation values of operators, normalization, particle in a box, particle in finite height barrier and finite well, reflection and transmission, Harmonic oscillator, particle in linearly varying potential, Infinite potential well, delta function potential. Time dependent Schrödinger equation, time evolution of stationary states: Infinite well and harmonic oscillator, wave packets and time evolution with example, group velocity. Crystals, one electron approximation, Bloch theorem, density of states in k space, effective mass theory, effective mass approximation in semiconductor heterostructures, density of states in energy, density of states in quantum well, K.P model for two-band semiconductor. Band structure calculations for cubic crystals, Nanostructures: quantum wire, quantum well, quantum dots |
| PHY F346 |
Laser Science and Technology |
3 0 3 |
|
Introduction to lasers, theory of radiation, laser basics, optical resonators, longitudinal / transverse modes, pumping of laser media, Line broadening mechanism, Transient behaviour : Q-switching, mode locking, devices, techniques. Types of lasers : solid state lasers, gas lasers, liquid lasers, semiconductor laser, x-ray laser, free electron laser, maser. Non-linear optics: Phase matching, second harmonic generation, third harmonic generation, difference frequency generation, optical parametric generation etc. Applications of lasers : Industry, medicine, biology, optical /quantum communication, thermonuclear fusion, isotope separation, holography, laser cooling etc. |
| PHY F412 |
Introduction to Quantum Field Theory |
3 1 4 |
|
Klein-Gordon equation, SU(2) and rotation group, SL(2,C) and Lorentz group, antiparticles, construction of Dirac spinors, algebra of gamma matrices, Maxwell and Proca equations, Maxwell's equations and differential geometry; Lagrangian Formulation of particle mechanics, real scalar field and Noether's theorem, real and complex scalar fields, Yang-Mills field, geometry of gauge fields, canonical quantization of Klein-Gordon, Dirac and Electromagnetic field, spontaneously broken gauge symmetries, Goldstone theorem, superconductivity. |
| PHY F413 |
Particle Physics |
3 1 4 |
|
Klein-Gordon equation, time-dependent non-relativistic perturbation theory, spinless electron-muon scattering and electron-positron scattering, crossing symmetry, Dirac equation, standard examples of scattering, parity violation and V-A interaction, beta decay, muon decay, weak neutral currents, Cabbibo angle, weak mixing angles, CP violation, weak isospin and hypercharge, basic electroweak interaction, Lagrangian and single particle wave-equation, U(1) local gauge invariance and QED, non-Abelian gauge invariance and QCD, spontaneous symmetry breaking, Higgs mechanism, spontaneous breaking of local SU(2) gauge symmetry. |
| PHY F415 |
General Theory of Relativity and Cosmology |
3 1 4 |
|
Review of relativistic mechanics, gravity as geometry, descriptions of curved space-time, tensor analysis, geodesic equations, affine connections, parallel transport, Riemann and Ricci tensors, Einstein’s equations, Schwarzschild solution, classic tests of general theory of relativity, mapping the universe, Friedmann- Robertson-Walker (FRW) cosmological model, Friedmann equation and the evolution of the universe, thermal history of the early universe, shortcomings of standard model of cosmology, theory of inflation, cosmic microwave background radiations (CMBR), baryogenesis, dark matter & dark energy. |
| PHY F416 |
Soft Condensed Matter Physics |
3 1 4 |
|
Forces, energies, timescale and dimensionality in soft condensed matter, phase transition, mean field theory and its breakdown, simulation of Ising spin using Monte Carlo and molecular dynamics, colloidal dispersion, polymer physics, molecular order in soft condensed matter – i) liquid crystals ii) polymer, supramolecular self assembly. |
| PHY F418 |
Lasers and Applications |
3 0 3 |
|
Properties of laser light, theories of some simple optical processes, basic principles of lasers, solid-state lasers, gas lasers, semiconductor lasers, free electron lasers, liquid, dye and chemical lasers, dynamics of laser processes, advances in laser physics, Q-switching, mode-locking (active and passive), saturable absorbers, Kerr lens mode locking, non-linear optics, laser spectroscopy, time resolved spectroscopy, multi-photon spectroscopy. |
| PHY F419 |
Advanced Solid State Physics |
3 1 4 |
|
Schrodinger field theory (second quantized formalism), Bose and Fermi fields, equivalence with many body quantum mechanics, particles and holes, single particle Green functions and propagators, diagrammatic techniques, application to Fermi systems (electrons in a metal, electron – phonon interaction) and Bose systems (superconductivity, superfluidity). |
| PHY F420 |
Quantum Optics |
3 0 3 |
|
Quantization of the electromagnetic field, single mode and multimode fields, vacuum fluctuations and zero-point energy, coherent states, atom - field interaction - semiclassical and quantum, the Rabi model, Jaynes-Cummings model, beam splitters and interferometry, squeezed states, lasers. |
| PHY F421 |
Advanced Quantum Mechanics |
3 1 4 |
|
Symmetries, conservation laws and degeneracies; Discrete symmetries - parity, lattice translations and time reversal; Identical particles, permutation symmetry, symmetrization postulate, two-electron system, the helium atom; Scattering theory - Lippman- Schwinger equation, Born approximation, optical theorem, eikonal approximation, method of partial waves; Quantum theory of radiation - quantization of electromagnetic field, interaction of electromagnetic radiation with atoms; relativistic quantum mechanics. |
| PHY F422 |
Group Theory and Applications |
3 1 4 |
|
Basic concepts – group axioms and examples of groups, subgroups, cosets, invariant subgroups; group representation – unitary representation, irreducible representation, character table, Schur’s lemmas; the point symmetry group and applications to molecular and crystal structure; Continuous groups – Lie groups, infinitesimal transformation, structure constants; Lie algebras, irreducible representations of Lie groups and Lie algebras; linear groups, rotation groups, groups of the standard model of particle physics. |
| PHY F423 |
Special Topics in Statistical Mechanics |
3 1 4 |
|
The Ising Model – Definition, equivalence to other models, spontaneous magnetization, Bragg- William approximation, Bethe- Peierls Approximation, one dimensional Ising model, exact solution in one and two dimensions; Landau’s mean field theory for phase transition – the order parameter, correlation function and fluctuation-dissipation theorem, critical exponents, calculation of critical exponents, scale invariance, field driven transitions, temperature driven condition, Landau-Ginzberg theory, two-point correlation function, Ginzberg criterion, Gaussian approximation; Scaling hypothesis – universality and universality classes, renormalization group; Elements of nonequilibrium statistical mechanics – Brownian motion, diffusion and Langevin equation, relation between dissipation and fluctuating force, Fokker-Planck equation |
| PHY F424 |
Advanced Electrodynamics |
3 0 3 |
|
Review of Maxwell’s equations – Maxwell’s equations, scalar and vector potentials, gauge transformations of the potentials, the electromagnetic wave equation, retarded and advanced Green’s functions for the wave equation and their interpretation, transformation properties of electromagnetic fields; Radiating systems – multipole expansion of radiation fields, energy and angular momentum of multipole radiation, multipole radiation in atoms and nuclei, multipole radiation from a linear, centre-fed antenna; Scattering and diffraction – perturbation theory of scattering, scattering by gases and liquids, scattering of EM waves by a sphere, scalar and vector diffraction theory, diffraction by a circular aperture; Dynamics of relativistic particles and EM fields – Lagrangian of a relativistic charged particle in an EM field, motion in uniform, static electromagnetic fields, Lagrangian of the EM fields, solution of wave equation in covariant form, invariant Green’s functions; Collisions, energy loss and scattering of a charged particle, Cherenkov radiation, the Bremsstrahlung; Radiation by moving charges – Lienard-Wiechert potentials and fields, Larmor’s formula and its relativistic generalization; Radiation damping – radiative reaction force from conservation of energy, Abraham-Lorentz model. |
| PHY F426 |
Physics of Semiconductor Devices |
3 0 3 |
|
Basics-Crystal structure, Wave Mechanics and the Schrodinger Equation, Free and Bound Particles, Fermi energy, Fermi-Dirac Statistics, Fermi level, Density of states, Band Theory of Solids, Concept of Band Gap, direct and indirect band gap, equation of motion, electron effective mass, concept of holes, Doping in semiconductors, Carrier transport - transport equations, Generation / Recombination Phenomena, Semiconductor processing and characterization, p-n junction, metal-semiconductor contacts, MOS capacitors, JFET, MESFET, MOSFET, Heterojunction devices, Quantum effect, nanostructures, Semiconductor and Spin Physics, Magnetic Semiconductors |
| PHY F428 |
Quantum Information Theory |
3 0 3 |
|
Classical Information, probability and information measures, methods of open quantum systems using density operator formalism, quantum operations, Kraus operators. Measurement and information, Entropy and information, data compression, channel capacity, Resource theory of quantum correlations and coherence, and some current issues. |
| PHY F431 |
Geometrical Methods in Physics |
3 0 3 |
|
Manifolds, tensors, differential forms and examples from Physics, Riemannian geometry, relevance of topology to Physics, integration on a manifold, Gauss theorem and Stokes’ theorem using integrals of differential forms, fibre bundles and connections, applications of geometrical methods in Classical and Quantum Mechanics, Electrodynamics, Gravitation, and Quantum field theory. Rotations in real complex and Minkowski spaces laying group theoretical basis of 3-tensors and 4 tensors and spinors, transition from a discrete to continuous system, stress energy tensor, relativistic field theory, Noether’s theorem, tensor and spinor fields as representation of Lorentz group, action for spin-0 and spin-1/2, and super-symmetric multiplet, introduction of spin-1, spin-2 and spin-3/2 through appropriate local symmetries of spin-0 and spin-1/2 actions. |