Differential and total scattering cross section, transformation from CM frame to Lab frame, solution of scattering problem by the method of partial wave analysis, expansion of a plane wave into a spherical wave and scattering amplitude, the optical theorem, Applications: square well potential and the hard sphere scattering of identical particles, energy dependence and resonance scattering, Breit-Wigner formula, quasi stationary states, Lippman-Schwinger equation, Born approximation and its validity for scattering problem, Coulomb scattering problem under first Born approximation in elastic scattering.

Attempt for relativistic formulation of quantum theory, The Klein-Gordon equation, Probability density and probability current density, solution of free particle KG equation in momentum representation, interpretation of negative probability density and negative energy solutions. Dirac relativistic equation and its general solution.

Properties of Dirac matrices and algebra of gamma matrices, non-relativistic correspondence of the Pauli equation (inclusive of electromagnetic interaction), Solution of free particle Dirac equation, orthogonality and completeness, relations for Dirac spinors, interpretation of negative energy solution, Lorentz covariance of Dirac equation, charge conjugation (C), Parity(P), time reversal (T) , CPT theorem, Zitterbewegung.

Classical radiation field, transversality condition, Fourier decomposition and radiation oscillators, Quantization of radiation oscillator, creation, annihilation and number operators, photon states, photon as a quantum mechanical excitations of the radiation field, fluctuations and the uncertainty relation, validity of the classical description, matrix element for emission and absorption, spontaneous emission in the dipole approximation, Rayleigh scattering. Thomson scattering and the Raman effect, Radiation damping and Resonance fluorescence.

S-matrix, S-matrix expansion, Wick's theorem, Diagrammatic representation in configuration space, the momentum representation, Feynman diagrams of basic processes. Applications of S-matrix formalism: The Coulomb scattering, Bhabha scattering, Compton scattering and Pair production.