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.
