Mathematics for Quantum Chemistry - N413033
Title: Matematika pro kvantovou chemii
Guaranteed by: Department of Mathematics (413)
Actual: from 2015
Semester: summer
Points: summer s.:5
E-Credits: summer s.:5
Examination process: summer s.:
Hours per week, examination: summer s.:2/2 C+Ex [hours/week]
Capacity: 24 / 30 (unknown)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
Level:  
For type:  
Note: course can be enrolled in outside the study plan
enabled for web enrollment
Guarantor: Turzík Daniel doc. RNDr. CSc.
Class: Předměty pro matematiku
Examination dates   Schedule   
This subject contains the following additional online materials
Annotation -
Last update: TAJ413 (19.07.2013)
To build a theoretical framework of quantum chemistry it is important to study properties of operators defined on state spaces. The course Mathematics for quantum chemistry introduces selected topics of functional analysis. It deals with linear spaces, linear operators and spectras of linear operators.
Aim of the course -
Last update: TAJ413 (19.07.2013)

Students will learn the basics of functional analysis: normed and Hilbert spaces, norms of operators and their spectra.

Literature -
Last update: TAJ413 (19.07.2013)

R: A. E. Taylor: Introduction to Functional Analysis, 2nd ed. Wiley New York, 1980, ISBN-13: 978-0471846468.

Learning resources -
Last update: Dubcová Miroslava RNDr. Ph.D. (18.07.2013)

http://www.vscht.cz/mat/Ostatni/MIII9-12k.pdf

http://www1.maths.leeds.ac.uk/~kisilv/courses/math3263m.html

http://www1.maths.leeds.ac.uk/~kisilv/courses/math3263m.pdf

Teaching methods -
Last update: Dubcová Miroslava RNDr. Ph.D. (18.07.2013)

Lectures and exercise classes.

Syllabus -
Last update: TAJ413 (19.07.2013)

1. Mathematical formulation of classical mechanics and quantum mechanics.

2. Normed linear spaces. Complete spaces. Banach spaces.

3. Spaces with scalar product. Hilbert spaces.

4. Examples. Spaces C(K), spaces c and l.

5. Summation of series, measure and integral, Lebesgue measure and integral. L-spaces.

6. Orthonormal bases of the Hilbert spaces. Fourier series expansion. Bessel inequality.

7. Linear operators and their norms. Dual spaces.

8. Linear forms on Hilbert spaces. Examples of dual spaces.

9. Hahn-Banach theorem and its corollaries.

10. Canonical embeddings, reflexive spaces and orthogonal projections.

11. Spectra of bounded linear operators. Point spectrum.

12. Compact operators and their spectra.

13. Banach algebras.

14. Spectral theory in Hilbert spaces.

Registration requirements -
Last update: TAJ413 (19.07.2013)

Mathematics I, Mathematics II

Teaching methods
Activity Credits Hours
Konzultace s vyučujícími 0,5 14
Účast na přednáškách 1 28
Příprava na přednášky, semináře, laboratoře, exkurzi nebo praxi 1 28
Příprava na zkoušku a její absolvování 1,5 42
Účast na seminářích 1 28
5 / 5 140 / 140
Coursework assessment
Form Significance
Regular attendance 25
Continuous assessment of study performance and course -credit tests 25
Oral examination 50