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Course, academic year 2023/2024
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Mathematics for Quantum Theory - NOFY074
Title: Matematika pro kvantovku
Guaranteed by: Department of Chemical Physics and Optics (32-KCHFO)
Faculty: Faculty of Mathematics and Physics
Actual: from 2021
Semester: summer
E-Credits: 2
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. Ing. Pavel Soldán, Dr.
doc. Ing. Lucie Augustovičová, Ph.D.
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.
Last update: T_KCHFO (01.05.2016)
Aim of the course -

To introduce mathematical foundations of quantum mechanics.

Last update: T_KCHFO (01.05.2016)
Course completion requirements -

The lecture course is concluded with an exam.

Last update: Soldán Pavel, doc. Ing., Dr. (29.04.2020)
Literature -

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

Last update: T_KCHFO (01.05.2016)
Teaching methods -

Lectures

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

Successfully passing an exam in this lecture course means correctly solving two problems, which are submitted to students in an electronic form before the term end and which correspond to the lecture topics read in the current academic year. When solving the problems, students can consult any literature source. Students can submit their exam-problem solutions electronically anytime before the term end (only as a pdf file) or hand them in in a written form at one of the offered exam days in the current exam period.

Last update: Soldán Pavel, doc. Ing., Dr. (29.04.2020)
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

Last update: T_KCHFO (01.05.2016)
Entry requirements -

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

Last update: T_KCHFO (01.05.2016)
 
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