Aims

The course is centered on the study of the essential tool of quantum mechanics, the Hilbert space. The abstract notions are brought progressively, starting from concrete cases ("special" functions; Fourier series) and are illustrated by applications taken from theoretical physics (in particular quantum mechanics).

Main themes

- Fourier series
- Special functions: orthogonal polynomials (Legendre, Laguerre, Hermite), Bessel functions
- Hilbert space
- Operators in Hilbert space, spectral theory, special types of operators
- Introduction to the theory of distributions

Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Prerequisites: candidature level in algebra, analyse and general physics.

Evaluation: written and oral examination.

Support: syllabus.

Openings: Teaching of quantum mechanics (PHYS 2290, PHYS 2300, PHYS 2310); Advanced formation on functional analyse and quantum theory (fields theory).