**Mathematical Physics: **Linear vector space; matrices; vector
calculus; linear differential equations; elements of complex analysis; Laplace
transforms, Fourier analysis, elementary ideas about tensors.

**Classical Mechanics: **Conservation laws; central forces, Kepler problem
and planetary motion; collisions and scattering in laboratory and centre of mass
frames; mechanics of system of particles; rigid body dynamics; moment of inertia
tensor; non inertial frames and pseudo forces; variational principle; Lagrange’s
and Hamilton’s formalisms; equation of motion, cyclic coordinates, Poisson
bracket; periodic motion, small oscillations, normal modes; special theory of
relativity – Lorentz transformations, relativistic kinematics, mass-energy
equivalence.

**
Electromagnetic Theory: **Solution of electrostatic and magnetostatic problems
including boundary value problems; dielectrics and conductors; Biot-Savart’s and
Ampere’s laws; Faraday’s law; Maxwell’s equations; scalar and vector potentials;
Coulomb and Lorentz gauges; Electromagnetic waves and their reflection,
refraction, interference, diffraction and polarization. Poynting vector,
Poynting theorem, energy and momentum of electromagnetic waves; radiation from a
moving charge.

**Physical basis of quantum mechanics; uncertainty principle; Schrodinger equation; one, two and three dimensional potential problems; particle in a box, harmonic oscillator, hydrogen atom; linear vectors and operators in Hilbert space; angular momentum and spin; addition of angular momenta; time independent perturbation theory; elementary scattering theory.**

Quantum Mechanics:

Quantum Mechanics:

**Laws of thermodynamics; macrostates and microstates; phase space; probability ensembles; partition function, free energy, calculation of thermodynamic quantities; classical and quantum statistics; degenerate Fermi gas; black body radiation and Planck’s distribution law; Bose-Einstein condensation; first and second order phase transitions, critical point.**

Thermodynamics and Statistical Physics:

Thermodynamics and Statistical Physics:

**Atomic and Molecular Physics:**Spectra of one- and many-electron atoms; LS and jj coupling; hyperfine structure; Zeeman and Stark effects; electric dipole transitions and selection rules; X-ray spectra; rotational and vibrational spectra of diatomic molecules; electronic transition in diatomic molecules, Franck-Condon principle; Raman effect; NMR and ESR; lasers.

**Elements of crystallography; diffraction methods for structure determination; bonding in solids; elastic properties of solids; defects in crystals; lattice vibrations and thermal properties of solids; free electron theory; band theory of solids; metals, semiconductors and insulators; transport properties; optical, dielectric and magnetic properties of solids; elements of superconductivity.**

Solid State Physics:

Solid State Physics:

**Nuclear and Particle Physics:**Nuclear radii and charge distributions, nuclear binding energy, Electric and magnetic moments; nuclear models, liquid drop model – semi-empirical mass formula, Fermi gas model of nucleus, nuclear shell model; nuclear force and two nucleon problem; Alpha decay, Beta-decay, electromagnetic transitions in nuclei; Ruther ford scattering, nuclear reactions, conservation laws; fission and fusion; particle accelerators and detectors; elementary particles, photons, baryons, mesons and leptons; quark model.

**Electronics:**Network analysis; semiconductor devices; Bipolar Junction Transistors, Field Effect Transistors, amplifier and oscillator circuits; operational amplifier, negative feedback circuits, active filters and oscillators; rectifier circuits, regulated power supplies; basic digital logic circuits, sequential circuits, flip-flops, counters, registers, A/D and D/A conversion.