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QUANTUM MECHANICS - II
Course Outline
Time Independent Perturbation Theory - applications to Fine Structure of Hydrogen Atom, Zeeman Effect.
Degenerate Perturbation Theory, Stark Effect.
Variational Principle and Applications.
WKB Approximation and Connection Formulae.
Time Dependent Perturbation Theory- Schrodinger, Heisenberg and Interaction Pictures.
Scattering Theory, Green's Functions
Texts / References:
R. Shankar, "Principles of Quantum Mechanics", Springer (1994)
J. J. Sakurai and J. J. Napolitano, “Modern Quantum Mechanics”, 2nd Edition, Pearson (2010)
D. J. Griffiths, "Introduction to Quantum Mechanics", 7th Edn., Pearson (2005)
E. Merzbacher, "Quantum Mechanics", 3rd Edn.. John Wiley (2003)
Bipin R. Desai, "Quantum Mechanics with Basic Field Theory", Cambridge (2010)
Steven Weinberg, "Lectures on Quantum Mechanics", Cambridge (2013)
1. Angular Momentum and its Addition : Angular Momentum -1 Discusses theory of Angular Momentum, Angular Momentum-II introduces addition of angular momentum and Clebsch-Gordan coefficients.
Power point slides : Angular Momentum - A review. Spherical Tensors
2. Wigner-Eckart Theorem: Introduces spherical tensors, reduced matrix elements and Wigner-Eckart Theorem.
3. Symmetry in Quantum Mechanics: Quantum transformations and symmetries, continuous symmetry, space and time translation, rotation, O(3), SO(3) and SU(2) symmetries; Discrete symmetry, space inversion and Parity, time reversal symmetry, charge conjugation.
4. Time Independent Perturbation Theory : Discussion of time independent perturbation theory, both non-degenerate and Degenerate perturbation theories, Fine structure of hydrogen energy levels, Stark Effect in hydrogen atom, Zeeman effect.
Mid-sem 2019 with solutions
5. Variational Principle : Upper bounds for Ground State Energy and the energy of the first excited state, Properties of the eig enstates state of one dimensional potential, Applications to Deuteron problem and Helium atom, Method of Linear Variation functions.
6. WKB Approximation: Asymptotic solutions, Turning points and connection formulae, Potential with one rigid wall, Potential with two rigid walls, Tunnelling through a barrier.
Midsem (Re-exam) with Solution
7. Time dependent Perturbation Theory: Basic formalism, constant and harmonic perturbation, Fermi’s Golden Rule, Berry Phase.
8. Semiclassical Theory of Radiation: Interaction of charged particle with electromagnetic field, Dipole approximation, Spontaneous and stimulated emission, Absorption, Einstein A and B coefficients, Laser Theory.
9. Scattering Theory I : Lippmann-Schwinger equation, Green’s function, Born approximation, Rutherford Scattering.
Solution (unedited)
10. Scattering Theory II : Method of Partial Waves, Optical Theorem, s-wave scattering from a hard sphere.