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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2020/2021

Advanced Topics of Quantum Theory

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Code Completion Credits Range Language
02PPKT ZK 2 2+0 Czech
Lecturer:
Pavel Exner (guarantor)
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 2020/2021:
Time-table is not available yet
Time-table for summer semester 2020/2021:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2021-01-27
For updated information see http://bilakniha.cvut.cz/en/predmet12076405.html