Advanced Quantum Mechanics
Credits: 3
Type: Compulsory
Duration: c1
COURSE INDEX
- Axiomátic Formulation. Von Neumann and Dirac formulations. Rigged Hilbert spaces. Proyectve representations. Wigner and Husimi transformations. Semiclasic limit. Operators.
- Collision theory. Green Functions. Analytic properties. Resonances and bound states. Moeller operators. Scattering matrix. Unitarity. Lippman-Schwinger equation. Approximation methods.
- Symmetries. Noether theorem. Symmetry breaking. Poincare Invariance. Relativistic Invariance: Klein-Gordon and Dirac equations.
- Density matrix. Pure and impure states. Quantum information.
- Advanced Topics: SUSY quantum mechanics. Feynman formulation.
BIBLIOGRAPHY
- Galindo y P. Pascual , Vols. I y II Mecánica Cuántica, Eudema (1990).
- Reed , B. Simon, Methods of Modern Mathematical Analysis , vols. I,II,II y IV (Academic Press)
- Chadan y P. C. Sabatier, Inverse Problems in Quantum Scattering Theory, Springer 1977.
- Levitan , I. S. Sargsjan, Sturm-Liouville and Dirac Operators, Kluwer , 1990
- The Schrödinger Equation, F. A. Brezin, M. A. Shubin, Kluwer , 1991
- J, von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton, 1996
- Gelfand , Shilov, Theory of Distributions, 5 vols.