Distributions. Elements of spectral theory. Complements of complex analysis.
Symmetries in classical mechanics and quantum mechanics. Magnetic monopoles. Periodic potentials. Adiabatic approximation. Metastable states. Path integral.
- Sakurai, Napolitano, Modern Quantum Mechanics, 3 ed., Cambridge University Press
- Konishi, Paffuti, Quantum Mechanics: A New Introduction, OUP Oxford
- Notes of the course
Learning Objectives
Knowledge of advanced mathematical methods and their application to topics in quantum mechanics.
Prerequisites
Good knowledge of the topics included in the course Mathematical Methods for Physics and in the first semester of the course Foundations of Theoretical Physics (basic principles of quantum mechanics)
Teaching Methods
Theoretical lessons and discussion of examples and exercises
Further information
CFU: 6
48 hours of lessons.
Type of Assessment
Oral exam (duration approx. 60 min). Discussion of subjects of the course. Evaluation of the language used in the discussion, determination of the level of understanding of the physical interpretation of the subjects and of the related mathematical aspects.
Course program
Distribution theory. Spectral theory, generalised eigenvectors, spectral decomposition of self-adjoint operators. Complements of complex analysis (cuts and multi-valued functions).
Symmetries in classical mechanics and quantum mechanics, conservation laws and their consequences. Magnetic monopoles. Periodic potentials. Adiabatic approximation, Berry phase. Metastable states, resolvent, dispersion relations. Introduction to the path integral.