Integrative teaching
Exercises
Examination procedure
Oral exam
Prerequisites
The course is mostly directed to Master-level students in Chemistry. A good knowledge of mathematical analysis and linear algebra is assumed.
Syllabus
1) Banach and Hilbert Spaces
2) Geometry of Hilbert space. Orthonormal bases.
3) Linear operators on Hilbert spaces. Bounded linear operators and functionals. Projectors.
4) Compact operators. Trace class operators.
5) Elements of spectral theory. Hilbert-Schmidt Theorem for compact self-adjoint operators.
6) Unbounded linear operators. Closed operators.
7) Spectral Theorem for unbounded self-adjoint operators. One-parameter groups of unitary operators. Stone's Theorem.
8) Quantum-mechanical applications and examples.
Bibliographical references
Sandro Graffi, Alcuni Aspetti Matematici della Meccanica Quantistica. Quaderni dell'Istituto Nazionale di Alta Matematica, Gruppo Nazionale di Fisica Matematica, 2004.
Other references will be provided during the course of the lectures.