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Course, academic year 2018/2019
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Mathematics for Quantum Theory - NOFY074
Title in English: Matematika pro kvantovku
Guaranteed by: Department of Chemical Physics and Optics (32-KCHFO)
Faculty: Faculty of Mathematics and Physics
Actual: from 2016
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: doc. Ing. Pavel Soldán, Dr.
Ing. Lucie Augustovičová, Ph.D.
Annotation -
Last update: T_KCHFO (01.05.2016)
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.
Aim of the course -
Last update: T_KCHFO (01.05.2016)

To introduce mathematical foundations of quantum mechanics.

Course completion requirements - Czech
Last update: doc. Ing. Pavel Soldán, Dr. (03.01.2018)

Předmět je zakončen ústní zkouškou.

Literature -
Last update: T_KCHFO (01.05.2016)

Jiří Blank, Pavel Exner, Miloslav Havlíček: Hilbert Space Operators in Quantum Physics, AIP Press, NY 1994; 2nd Ed. Springer Netherlands 2008

Teaching methods -
Last update: T_KCHFO (01.05.2016)

Lectures

Requirements to the exam -
Last update: T_KCHFO (01.05.2016)

Oral exam of the lecture topics.

Syllabus -
Last update: T_KCHFO (01.05.2016)

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

Entry requirements -
Last update: T_KCHFO (01.05.2016)

Reasonable knowledge of the first year linear algebra and mathematical analysis.

 
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