General properties of the Schrodinger Equation, Ehrenfest theorem, Evolution operator, Schrodinger, Heisenberg, and Interaction pictures, Conservative systems, Density Operator, Propagator, Quantum entanglement, The EPR argument, Bell's inequalities, Approximation methods: perturbation theory, variational method, WKB method
Symmetries in Quantum Mechanics General discussion, Translational symmetry, Rotational symmetry, Parity, Time-reversal symmetry, Gauge symmetry
Two-State Systems General discussion, Rabi's formula, Spin-1 particles, Larmor precession and magnetic resonance, System of two spin-1 particles
Systems in One Dimension Harmonic oscillator, Coherent and squeezed states, Delta potential, Square potential well and infinite potential well, Potential barrier and tunneling, Periodic potential, Bloch's Condition, Kronig-Penney model
Systems in Two or Three Dimensions General properties of the angular momentum, Landau Levels, Aharonov- Bohm effect, Particle in a central potential, Rotational-vibrational levels of diatomic molecules, Hydrogen atom, Fine structure, Zeeman effect
R. Shankar, "Principles of Quantum Mechanics", Plenum Press, 1994
J. J. Sakurai, "Modern Quantum Mechanics", The Benjamin, 1985
C. Cohen-Tannoudji, "Quantum Mechanics", John Wiley, 1977
R. L. Liboff, "Introductory Quantum Mechanics", Addison-Wesley, 1980
E. Merzbacher, "Quantum Mechanics", John Wiley & Sons, 1970
2. Mathematical Methods
Complex variables: Set theoretic foundation, concepts of curves, limits, derivatives, analyticity, sequences, series, inverse of a function, singularities and contour integration, conformal mapping
Differential equations: Ordinary differential equations, hypergeometric equation, partial differential equations, method of characteristics, boundary value problems
Integral equations: Fredholm equation, iterative solution, Green functions
"Mathematical Methods for Physicists", G. Arfken
"Methods of Theoretical Physics" vol. 1 and 2, Morse and Feshbach
3. Classical Electrodynamics
Electrostatics, Boundary value problems, Multipole expansion, macroscopic media
Maxwell equations, gauge invariance, Poynting vector, magnetic monopole
Electromagnetic waves, reflection, refraction, waves in conducting or dissipative medium, wave guides, Radiating systems
Covariant formulation, special relativity, Lagrangian and Hamiltonian formulations, Dynamics of relativistic particles and electromagnetic fields
Geometry of Gauge Fields (Special Topic)
Classical Electrodynamics by J.D. Jackson (Main textbook)
Landau and Lifshitz, Vol.2 and Vol. 8
Classical Electrodynamics by W. Greiner
4. Statistical Physics
Basic concepts in thermodynamics, Entropy, Thermodynamic potentials.
Basic assumption of equilibrium statistical physics, Calculation of partition function under various constraints (constant energy, temperature, chemical potential)
Classical and quantum non-interacting particles and spins.
Fluctuation, stability, response and correlation.
Classical gases and liquids, radial distribution function, Ornstein-Zernike theory, van der Waal equation, liquid gas transition.
Models of interacting spins on a lattice. Transfer matrix.
Mean field theory.
Systematics of phase transitions, critical exponents, Ginsburg Landau theory, Scaling.
"Statistical Mechanics", R. K. Pathria
"Statistical Mechanics", K. Huang
"Introduction to Modern Statistical Mechanics", D. Chandler (Sections 1, 2 and 3 will be covered mainly through problems.)
5. Advanced Quantum Mechanics
Books which have good discussions of the relevant topics are mentioned topic-wise.
N-particle systems (Shankar, Wieder). N-particle Hilbert space, direct product space, N-particle Schrodinger equation.
Identical particles (Shankar, Greiner, Gasiorowicz): Symmetric and antisymmetric states (bosons and fermions), Pauli exclusion principle, spin-statistics theorem, normalization of states, Slater determinant, permutation operator, exchange degeneracy.
Second quantization (Galindo & Pascual, Merzbacher): Fock space, boson case, fermions, transformation of basis, dynamical variables, continuous one-particle spectrum case.
Relativistic Quantum Mechanics, early attempts (Bjorken & Drell, Sakurai): Klein-Gordon equation, negative energy and probability density.
Dirac equation (Bjorken & Drell, Sakurai, Itzykson & Zuber, Gross): Representation independence, relativistic covariance, bilinear covariants, Clifford algebra, non-relativistic approximations, plane-wave solutions, constants of motion, positron spinors and projection operators, Zitterbewegung, Klein's paradox, importance of negative energy solutions, Weyl equation and chiral transformations, electromagnetic coupling, approximate Hamiltonian for electrostatic case, Thomas term, Darwin term, Foldy-Wouthuysen transformation, Hole theory and positron, charge conjugation, time reversal and PCT, Hydrogen atom in Dirac theory, fine structure.
Path integral quantization (Shankar, Feynman & Hibbs): Propagator in path integral approach, free particle propagator, equivalence of path integral method to the Schrodinger equation, propagator for particle in a potential, harmonic oscillator, evaluation of path integral by Fourier series.
Aharanov-Bohm effect (Shankar).
Scattering Theory (Schiff)
6. Field Theory
Single particle relativistic wave equation
Prediction of antiparticle
Construction of Dirac spinors
Non-relativistic limit and the electron magnetic moment
Maxwell and Proca equations
Lagrangian formulation, symmetries and gauge fields
Lagrangian formulation of particle mechanics
The real scalar field: variational principle and Noether's theorem
Complex scalar and Electromagnetic fields
Canonical quantisation and particle interpretation
The real Klein-Gordon equation
The complex scalar Klein-Gordon equation
The Dirac field
The electromagnetic field
Interacting field and Feynman diagrams
Perturbation theory - philosophy and examples
Perturbative expansion of correlation functions
Cross sections and S-matrix
Computing S-matrix elements from Feynman diagrams
Feynman rules for fermions
Feynman rules for quantum electrodynamics
Elementary processes of quantum electrodynamics
e+e- ! μ+μ-: Introduction
e+e- ! μ+μ-: Helicity structure
e+e- ! μ+μ-: Non-relativistic limit
Radiative corrections (special topics)
Quantum Field Theory by L. Ryder, Academic Press (1989)
Quantum Field Theory by M. Peskin and D. Schroder Addison-Wesley (1995)
Gauge Theory of Elementary Particle Physics by T. Cheng and L. Li, Clarendon Press (1984)
7. Computational Physics
Basics ( fortran, representation of numbers in computers, loss of accuracy and propagation of errors, simple test programs )
Interpolation (Lagrange), sorting, pitfalls of interpolation, differentiation
Integration, quadratures, Monte Carlo
Differential equations (1-d), initial value, boundary value and eigenvalue problems
Matrices, products and sums, diagonalization, inversion
Random number generators, numerical simulations
Data fitting, chi-squares, K-S method, goodness of fit
Latex, MATHEMATICA, MAPLE, matlab, scilab etc Reference: "Numerical Recipes — The Art of Scientific Computing", W. H. Press, S. A. Teukelsky, W. T. Vellerling and B. P. Flannery
8. Condensed Matter Physics
Elementary constituents of solids: Ions and electrons. Adiabatic approximation.
Dynamics of electrons in a solid: Free electron model (classical and quantum), Drude theory,Weidenann-Franz law and electrical properties of solids.
Structure of crystalline solids: Lattice in real space, reciprocal lattice, X-ray and neutron scattering.
Dynamics of electrons (continued): Periodic potential, Bloch's theorem, energy bands and classification of solids (metals, semiconductors and insulators), electron correlation, Mott insulator.
Dynamics of ions: Lattice vibrations (phonons). Lattice specific heat (Debye model). Thermal expansion and thermal conductivity. Soft modes and structural phase transitions.
Semiconductors: intrinsic and extrinsic semiconductors. Law of mass action. Impurity bands, holes, excitons. p-n junctions, MOSFET, quantum wells and super lattices.
Superconductivity: The phenomenon (experimental observations). Thermodyanomics of superconductors. Superconductivity as a phase transition. Type-I, Type-II superconductors. Landon theory and Ginzburg-Landau theory (brief discussion). Cooper pairs and BCS theory of superconductivity (basic ideas)- brief account of recent developments
Magnetism: Magnetic phase transitions. Para, Ferro and Antiferro-magnetism. Spin waves, itinerant magnetism in metals and Pauli paramagnetism.
Surfaces: Surface states, behavior of physical properties on or near the surface. Books: "Solid State Physics", N. W. Ashcroft and N. D. Mermin
9. Nuclear Physics
NN interaction: symmetries, basics, low energy scattering and shape independence, meson theory and properties of NN interaction.
Nuclear systematics: masses, radii, shapes, magnetic and quadrupole moments, shell structure, radioactivity, fission
Basics of shell model, Hartree-Fock, pairing, rotational and vibrational spectra, giant resonances, halo nuclei
Nuclear Reactions: resonances and compound nucleus, direct reactions ( inelastic, stripping, pickup etc ), extracting nuclear information from reactions
Quark models ( bag ), quark equation of state, relativistic heavy ion collisions, signatures of QGP
"Structure of Nucleus", Preston and Bhaduri
"Theoretical Nuclear Physics", Blatt and Weisskopf
"Nuclear Structure" Bohr and Mottelson
"Nuclear Models" Greiner and Eisenberg
"Physics of Quark Gluon Plasma" Muller
10. Particle Physics
Lie Groups and Lie Algebras: Representation Theory, Young Tableau
Hadron Specroscopy: Eight-fold way, Quark Model
S-Matrix, Cross-section and Decay Rate: General discussion, Feynman rules, sample calculations
Broken and Unbroken Symmetries in Field Theory: Global and local symmetries, Goldstone and Higgs phenomena
Standard Model: Electroweak Model, Quantum Chromodynamics
Beyond Standard Model: Comments on Grand Unification, Supersymmetry, String theory
F. Halzen and A. D. Martin, 'Quarks and Leptons', John Wiley & Sons, 1984
T. P. Cheng and L. F. Lee, 'Gauge Theory of Elementry Particle Physics', Oxford Univ Press 1984.
G. Kane, 'Modern elementary particle physics', Addison-Wesley, 1987
D. Perkins, 'Introduction to High Energy Physics', Addison Wesley, 1987
11. Experimental Physics
Interactions of Charged Particles, Photons and Neutrons with Matter: A) Rutherford Scattering and Its Applications. B) Scattering of Photons i) Elastic Scattering - Bragg Diffraction And Its Applications ii) Inelastic Scattering, Compton Scattering And Applications.
Introduction to Particle Accelerators
Nuclear Radiation Detectors ( semiconductor, gas, scintillation and other advanced detectors )
Pulse Processing Techniques and Nuclear Instrumentation
Counting Statistics and Error Analysis
"Radiation Detection and Measurement", G. F. Knoll
"Techniques for Nuclear and Particle Physics Experiments", W. R. Leo
12. Laboratory Experiments
Gamma-ray spectroscopy – Energy calibration, Identifying unknown source – Identification of spectral features – Attenuation experiment
Compton scattering - angle dependence
Temperature dependence of resistivity of metals and semiconductors
Muon life time measurement
Charged particle spectroscopy with semiconductor detectors