Course Details
Subject {L-T-P / C} : PH4006 : Quantum Mechanics - II { 3-1-0 / 4}
Subject Nature : Theory
Coordinator : Prof. Sasmita Mishra
Syllabus
Approximate Method : Time independent perturbation theory :1st and 2nd order correction for non-degenerate case, application to one dimensional quantum harmonic oscillator, quadratic 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 (relativistic correction and spin-orbit interaction), Zeeman effect (weak field and strong field), brief discussion on the intermediate field Zeeman effect, linear Stark effect. Semiclassical WKB approximation. General principle of variational methods, identical particles, application of variational method to Helium atom, H2+ molecule ion. Time dependent potential and interaction picture, time dependent two state problems, spin magnetic resonance, MASER. Time dependent perturbation theory-transition probability, Fermi’s golden rule, application to constant perturbation, harmonic perturbation, interactions with classical radiation field, energy shift and decay width. Atom in a radiation field, electric dipole approximation, selection rules, photo-electric effect. 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.
Course Objectives
- Get familiar with different approximation methods in Quantum Mechanics and solving problems.
- Getting familiar with scattering theory and its applications.
- Getting familiar with time-independent and time-dependent perturbation theory and its application to atomic Physics
Course Outcomes
The course prepares the student to study some of the advanced courses based on microscopic principles. Also, it prepares the <br />student to appreciate some of the ongoing research in various domains.
Essential Reading
- D. J. Griffith, Introduction to Quantum Mechanics, Pearson, 2nd Edition (2007)
- J. J. Sakurai, Jim Napolitano, Modern Quantum Mechanics, 3rd ed, Cambridge University press
Supplementary Reading
- C. Cohen-Tannoudji, Quantum Mechanics, Volume 1: Basic Concepts, Tools, and Applications, 2nd ed., Wiley
- R. Shankar, Principles of Quantum Mechanics, Plenum Publishers, 2nd Edition (1994)