Syllabus
1. Hilbert spaces
2. Space of quadratically integrable functions
3. Orthogonal polynomials
4. Linear operators in Hilbert spaces
5. Spectra of linear operators
6. Symmetric and self-adjoint operators
7. Differential operators
8. Symmetric and self-adjoint differential operators
9. Spectra of self-adjoint operators
10. Distributions
11. Dirac delta function
Annotation
Lecture course is mainly for the 2nd year students in Physics. It complements the course Introduction to quantum mechanics and the following courses.
Its aim is to provide students with basic mathematical foundations of quantum mechanics. The theory will be accompanied by various examples.