Syllabus

Module 1: (12 hours)
Many-particle systems: Schrödinger equations, interchange symmetry, systems of distinguishable and non-interacting particles, Identical particles: exchange degeneracy, symmetrization postulates, construction of symmetric and anti- symmetric wave-functions, systems of identical and non-interacting particles, Pauli exclusion principle.

Module 2: (8 hours)
Time independent perturbation theory: 1st and 2nd order correction for non-degenerate case, application to one dimensional quantum harmonic oscillator, Stark effect, general principle of 1st order perturbation theory for degenerate case, application to the simple case of doubly degenerate problem, fine structure of Hydrogen atom spectrum, weak and strong field Zeeman effect, brief discussion on the intermediate field Zeeman effect.

Module 3: (8 hours)
Approximation Methods: Variational Method: general principle of variational method and application to Helium atom, H2+ molecule ion, general formalism of semi-classical W-K-B approximation, bound States for potential Wells with no, one and two rigid Walls, tunneling through a potential barrier, brief discussion on Gammow theory of alpha-decay.

Module 4: (12 hours)
Time-dependent perturbation theory: The Schrödinger, the Heisenberg and the interaction picture, time dependent perturbation theory-transition probability, adiabatic and sudden approximation, classical treatment of the incident radiation, quantization of the electromagnetic field, transition rates for absorption and emission of radiation, transition rates within the dipole approximation, the Electric dipole selection rules, spontaneous emission.

Module 5: (8 hours)
Scattering theory: collision cross section, scattering amplitude, the Born approximation, optical theorem, method of partial wave expansion and its application to scattering from hard sphere, scattering at low energies, s-wave scattering from a square well, resonant scattering and Breit-Wigner formula, optical theorem.

To learn multi-particles quantum mechanical systems.

To learn the etime independent perturbation theory.

To learn various approximation methods.

Time-dependent perturbation theory.

5. To learn scattering principles.

At the end of the course, students will be able to:
CO1: Solve the Schrodinger equation for multi-particle systems.

CO2: Use time independent perturbation theory to solve quantum mechanical problems.

CO3: Solve quantum mechanical problems using various approximation methods.

CO4: Apply time dependent approximation method in solving problems.

CO5: Comprehend the application of scattering theory.

N. Zettili, Quantum Mechanics: Concepts and Applications, Wiley , 2nd Edition (2009).

D. J. Griffith and D. F. Schroeter, Introduction to Quantum Mechanics, Cambridge University Press , 3rd Edition (2018).

C. Cohen-Tannoudji, Bernard Diu, Frank Laloe, Quantum Mechanics, Volume 1: Basic Concepts, Tools, and Applications, John Willey-VCH , 2nd Edition (2019).

J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics, Cambridge University Press , 3rd Edition (2020).