Systems of identical particles: the principle of indistinguishability. Exchange Operators. Exchange degeneracy and the postulate of symmetrization.
Symmetries in Quantum Mechanics: symmetry transformations and operators that represent symmetry transformations. Symmetry groups. Groups of continuous transformations: generators and the maximum set of operators that commute. The decomposition of the Hilbert space in invariant subspaces. Operators for finite transformations and their relationship with generators. Lie algebras. Casimir operators. Discrete symmetry transformations. Scalar, pseudoscalar, vector and pseudo vector operators and selection rules. The temporal inversion. The Kramer degeneration of Kramer.
Theory of Collisions: cross sections and scattering amplitudes. Dispersion by a central potential, phase shifts partial wave decomposition. Unitarity. Potentials of finite range.
Bibliography of reference
B. H. Bransden, C. J. Joachain, Physics of Atoms and Molecules, Longman Group Limite, 1983
A. Z. Capri, Nonrelativistic Quantum Mechanics, Benjamin/Cummings Publishing Company, 1985
C. Cohen-Tannoudji, B. Diu, F. Laloë, Mécanique Quantique, Hermann, Paris, 1977
L. D. Landau, E. M. Lifshitz, Quantum Mechanics (non-relativistic theory), Pergamn Press, 1997
A. Messiah, Quantum Mechanics, Dover Publications, N. Y., 1999
J. J. Sakurai, Moderm Quantum Mechanics, Addison-Wesley, 1993