Advanced Topics of Quantum Theory

Course guarantor:

Pavel Exner

Lecturer:

Pavel Exner

Tutor:

Supervisor:

Department of Physics

Synopsis:

Linear operators in Hilbert spaces, the uncertainty relations, the canonical commutational relations, the Stone theorem, algebras of observables, the Schrödinger operators. There is an overlap with 01KF, contents is modified according to students´ requirements.

Requirements:

02KVAN, 02KVAN2

Syllabus of lectures:

1. Hilbert spaces and linear operators.

2. Spectral theory of self-adjoint operators.

3. Operator algebras and sets.

4.-5. States and observables. Postulates of quantum mechanics.

6. Coordinates and momentum. Weyl relations.

7. Time evolution. Dynamical postulate.

8. Infinite number of degrees of freedom.

9. Schrödinger operators.

10. Scattering theory.

Syllabus of tutorials:

Study Objective:

Knowledge:

Understanding of mathematical foundations of quantum mechanics

Skills:

Applications to spectral theory of selfadjoint operators in quantum mechanics

Study materials:

Key references:

[1] J. Blank, P. Exner, M. Havlíček: Hilbert Space Operators in Quantum Physics, American Institute of Physics, 1993

Recommended references:

[2] J.M. Jauch: Foundations of quantum mechanics, Addison-Wesley, Reading (MA) 1968

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Matematická fyzika (elective course)