# PAPER-I

## Electromagnetic Theory
Electrostatics

Gauss� Law and its applications

Laplace and Poisson equations,
boundary value problems

Magnetostatics: Biot-Savart law, Ampere's theorem,
electromagnetic induction

Maxwell's equations in free space and linear isotropic
media

boundary conditions on fields at interfaces

Scalar and vector potentials

Gauge invariance

Electromagnetic waves in free space, dielectrics, and
conductors

Reflection and refraction, polarization, Fresnel�s Law, interference,
coherence, and diffraction

Dispersion relations in plasma

Lorentz invariance of
Maxwell�s equations

Dynamics of charged particles in static and uniform
electromagnetic fields

Radiation from moving charges, dipoles and retarded
potentials.

## Electronics

hysics of P-N junction, Diode as a circuit element, clipping and clamping,
Rectification, Zener regulated power supply Transistor as a circuit element, CC,
CB and CE configuration, Transistor as a switch, Feedback in amplifiers

Operational amplifiers and its applications, inverting and non-inverting
amplifiers, adder, integrator differentiator, wave form generator, multivibrators,
comparator, Schmidt trigger

Digital integrated circuits : NAND and NOR gates
as building blocks, X-OR gate, Half and Full adder circuits Flip � Flops, counters
and registers.

## Circuit Analysis

Kirchhoff's laws and their applications

Thevenin�s and Norton�s Theorem,
Maximum Power Transfer Theorem, Superposition Theorem, T and PI
Network, Mean and rms values in AC circuits

LR CR and LCR circuitsseries
and parallel resonance

Quality factor

Principal of transformer.

## Atomic & Molecular Physics

Quantum states of an electron in an atom

Electron spin

Stern-Gerlach
experiment

Spectrum of Hydrogen, helium and alkali atoms

Relativistic
corrections for energy levels of hydrogen

Hyperfine structure and isotopic shift

width of spectral lines

LS & JJ coupling

Zeeman, Paschen Back & Stark effect

X-ray spectroscopy

Electron spin resonance, Nuclear magnetic resonance,
chemical shift

Rotational, vibrational, electronic, and Raman spectra of diatomic
molecules

Frank � Condon principle and selection rules

Spontaneous and
stimulated emission, Einstein A & B coefficients

Lasers, optical pumping,
population inversion, rate equation.

## Condensed Matter Physics

Bravais lattices

Reciprocal lattice, diffraction and the structure factor

Bonding
of solids

Elastic properties, phonons, lattice specific heat

Free electron theory
and electronic specific heat

Response and relaxation phenomena

Drude model
of electrical and thermal conductivity

Hall effect and thermoelectric power

Diamagnetism, paramagnetism, and ferromagnetism

Electron motion in a
periodic potential, band theory of metals, insulators and semiconductors

Superconductivity, type � I and type - II superconductors, Josephson junctions.

# Paper-II

## Mathematical Methods of Physics

Dimensional analysis

Vector algebra and vector calculus

Linear algebra,
matrices, Cayley Hamilton theorem, eigenvalue problems

Linear differential
equations

Special functions (Hermite, Bessel, Laguerre and Legendre)

Fourier
series, Fourier and Laplace transforms

Elements of complex analysis

Elementary ideas about tensors

Introductory group theory

Elements of
computational techniques: roots of functions, interpolation, extrapolation,
integration by trapezoid and Simpson�s rule, solution of first order differential
equations using Runge-Kutta method

Finite difference methods

Elementary
probability theory, random variables, binomial, Poisson and normal
distributions.

## Classical Mechanics

Newton�s laws

Phase space dynamics, stability analysis

Central-force motion

Two-body collisions, scattering in laboratory and centre-of-mass frames

Rigid
body dynamics, moment of inertia tensor, non-inertial frames and pseudoforces

Variational principle, Lagrangian and Hamiltonian formalisms and equations of
motion

Poisson brackets and canonical transformations

Symmetry, invariance
and conservation laws, cyclic coordinates

Periodic motion, small oscillations
and normal modes

Special theory of relativity, Lorentz transformations,
relativistic kinematics and mass�energy equivalence.

## Quantum Mechanics

Wave-particle duality

Wave functions in coordinate and momentum
representations

Commutators and Heisenberg's uncertainty principle

Matrix
representation

Dirac�s bra and ket notation

Schroedinger equation (timedependent
and time-independent)

Eigenvalue problems such as particle-in-abox,
harmonic oscillator, etc.

Tunneling through a barrier

Motion in a central
potential

Orbital angular momentum, Angular momentum algebra, spin

Addition of angular momenta

Hydrogen atom, spin-orbit coupling, fine
structure

Time-independent perturbation theory and applications

Variational
method

WKB approximation

Time dependent perturbation theory and Fermi's
Golden Rule

Selection rules

Semi-classical theory of radiation

Elementary
theory of scattering, phase shifts, partial waves, Born approximation

Identical
particles, Pauli's exclusion principle, spin-statistics connection

Relativistic
quantum mechanics: Klein Gordon and Dirac equations.

## Thermodynamic and Statistical Physics

Laws of thermodynamics and their consequences

Thermodynamic potentials,
Maxwell relations

Chemical potential, phase equilibria

Phase space, microand
macrostates

Microcanonical, canonical and grand-canonical ensembles and
partition functions

Free Energy and connection with thermodynamic quantities

First- and second-order phase transitions

Classical and quantum statistics, ideal
Fermi and Bose gases

Principle of detailed balance

Blackbody radiation and
Planck's distribution law

Bose-Einstein condensation

Random walk and
Brownian motion

Introduction to nonequilibrium processes

Diffusion
equation.

## Nuclear and Particle Physics

Basic nuclear properties: size, shape, charge distribution, spin and parity

Binding energy, semi-empirical mass formula

Liquid drop model

Fission and
fusion

Nature of the nuclear force, form of nucleon-nucleon potential

Chargeindependence
and charge-symmetry of nuclear forces

Isospin

Deuteron
problem

Evidence of shell structure, single- particle shell model, its validity
and limitations

Rotational spectra

Elementary ideas of alpha, beta and gamma
decays and their selection rules

Nuclear reactions, reaction mechanisms,
compound nuclei and direct reactions

Classification of fundamental forces

Elementary particles (quarks, baryons, mesons, leptons)

Spin and parity
assignments, isospin, strangeness

Gell-Mann-Nishijima formula

C, P, and T
invariance and applications of symmetry arguments to particle reactions, parity
non-conservation in weak interaction

Relativistic kinematics.