**PART ‘B’ ADVANCED**

**A. ** ** Mathematical Methods of Physics :**
Green’s function. Partial differential equations (Laplace, wave and heat equations in two and three
dimensions). Elements of computational techniques: root of functions, interpolation, extrapolation,
integration by trapezoid and Simpson’s rule, Solution of first order differential equation using RungeKutta method. Finite difference methods. Tensors. Introductory group theory: SU(2), O(3).

**B. ** **Classical Mechanics:** Dynamical systems, Phase space dynamics, stability analysis. Poisson brackets and canonical
transformations. Symmetry, invariance and Noether’s theorem. Hamilton-Jacobi theory.

**C. ** **Electromagnetic Theory:** Dispersion relations in plasma. Lorentz invariance of Maxwell’s equation. Transmission lines and wave
guides. Radiation- from moving charges and dipoles and retarded potentials.

**D. ** **Quantum Mechanics :** Spin-orbit coupling, fine structure. WKB approximation. Elementary theory of scattering: phase shifts,
partial waves, Born approximation. Relativistic quantum mechanics: Klein-Gordon and Dirac equations.
Semi-classical theory of radiation.

**E. ** **Thermodynamic and Statistical Physics:** First- and second-order phase transitions. Diamagnetism, paramagnetism, and ferromagnetism. Ising
model. Bose-Einstein condensation. Diffusion equation. Random walk and Brownian motion.
Introduction to nonequilibrium processes.

**F. ** **Electronics and Experimental Methods:** Linear and nonlinear curve fitting, chi-square test. Transducers (temperature, pressure/vacuum, magnetic
fields, vibration, optical, and particle detectors). Measurement and control. Signal conditioning and
recovery. Impedance matching, amplification (Op-amp based, instrumentation amp, feedback), filtering
and noise reduction, shielding and grounding. Fourier transforms, lock-in detector, box-car integrator,
modulation techniques.

High frequency devices (including generators and detectors).

**G. ** **Atomic & Molecular Physics
:** Quantum states of an electron in an atom. Electron spin. Spectrum of helium and alkali atom. Relativistic
corrections for energy levels of hydrogen atom, hyperfine structure and isotopic shift, width of spectrum
lines, LS & JJ couplings. Zeeman, Paschen-Bach & Stark effects. Electron spin resonance. Nuclear
magnetic resonance, chemical shift. Frank-Condon principle. Born-Oppenheimer approximation.
Electronic, rotational, vibrational and Raman spectra of diatomic molecules, selection rules. Lasers:
spontaneous and stimulated emission, Einstein A & B coefficients. Optical pumping, population
inversion, rate equation. Modes of resonators and coherence length.

**H. ** **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. Electron motion in a periodic potential, band theory of solids: metals, insulators
and semiconductors. Superconductivity: type-I and type-II superconductors. Josephson junctions.
Superfluidity. Defects and dislocations. Ordered phases of matter: translational and orientational order,
kinds of liquid crystalline order. Quasi crystals

**I. ** **Nuclear and Particle Physics:** Basic nuclear properties: size, shape and charge distribution, spin and parity. Binding energy, semiempirical mass formula, liquid drop model. Nature of the nuclear force, form of nucleon-nucleon
potential, charge-independence and charge-symmetry of nuclear forces. 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. Fission and fusion. Nuclear reactions,
reaction mechanism, compound nuclei and direct reactions.

Classification of fundamental forces. Elementary particles and their quantum numbers (charge, spin,
parity, isospin, strangeness, etc.). Gellmann-Nishijima formula. Quark model, baryons and mesons. C, P,
and T invariance. Application of symmetry arguments to particle reactions. Parity non-conservation in
weak interaction. Relativistic kinematics.

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