PH5170 Quantum Mechanics II

Course Details

Orbital and spin angular momentum. Angular momentum algebra. Eigenstates and eigenvalues of angular momentum. Addition of angular momenta, Clebsch-Gordon coefficients. Irreducible tensor operators and the Wigner-Eckart theorem.
Systems of identical particles. Symmetric and antisymmetric wavefunctions. Bosons and Fermions. Pauli's exclusion principle. Second quantization, occupation number representation. Non-relativistic scattering theory. Scattering amplitude and cross- section. The integral equation for scattering. Born approximation. Partial wave analysis. The optical theorem.
Elements of relativistic quantum mechanics. The Klein-Gordon equation. The Dirac equation. Dirac matrices, spinors. Positive and negative energy solutions, physical interpretation. Nonrelativistic limit of the Dirac equation.

Course References:

1. J.J. Sakurai Modern Quantum Mechanics, Benjamin / Cummings (1985).
2. P.A.M. Dirac, The Principles of Quantum Mechanics, Oxford University Press (1991 ).
3. L.D.Landau and E.M. Lifshitz, Quantum Mechanics -Nonrelativistic Theory, 3rd Edition, Pergamon (1981 ).
4. P.M. Mathews and K. Venkatesan, A Textbook of Quantum Mechanics, Tata McGraw Hill (1977).
5. J. Bjorken and S. Drell, Relativistic Quantum Mechanics, McGraw-Hill (1965).
6. A. Messiah, Quantum Mechanics, Vols. 1 and 2, North Holland (1961 )