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Mathematics for Quantum Chemistry - N413033

Title:	Matematika pro kvantovou chemii
Guaranteed by:	Department of Mathematics (413)
Faculty:	Faculty of Chemical Engineering
Actual:	from 2021
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 [HT]
Capacity:	unknown / unknown (unknown)
Min. number of students:	unlimited
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Level:
Is provided by:	B413012
For type:

Guarantor:	Turzík Daniel doc. RNDr. CSc.
Class:	Předměty pro matematiku

Examination dates Schedule

Annotation -

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.

Last update: TAJ413 (19.07.2013)

Aim of the course -

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

Last update: TAJ413 (19.07.2013)

Literature -

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

Last update: TAJ413 (19.07.2013)

Learning resources -

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

Last update: Dubcová Miroslava (18.07.2013)

Teaching methods -

Lectures and exercise classes.

Last update: Dubcová Miroslava (18.07.2013)

Syllabus -

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.

Last update: TAJ413 (19.07.2013)

Registration requirements -

Mathematics I, Mathematics II

Last update: TAJ413 (19.07.2013)

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