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Course, academic year 2018/2019
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Quantum Mechanics - NUFY100
Title in English: Kvantová mechanika
Guaranteed by: Department of Physics Education (32-KDF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: summer
E-Credits: 8
Hours per week, examination: summer s.:4/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: RNDr. Zdeňka Koupilová, Ph.D.
RNDr. Vojtěch Kapsa, CSc.
RNDr. Petr Kácovský, Ph.D.
Classification: Physics > Teaching
Annotation -
Last update: T_KDF (12.05.2014)
Lecture of fundamentals of quantum mechanics for future physics teachers.
Aim of the course -
Last update: T_KDF (12.05.2014)

The lecture is aimed at an understanding the physical nature of quantum mechanics (QM) and its significance in the modern physics, like understanding of basic terms and postulates of QM including Schrödinger equation, solving selected applications: potential box, harmonic oscillator, hydrogen atom, quantum tunnelling, spin, approximate methods and multiparticle problems.

Course completion requirements - Czech
Last update: RNDr. Jitka Houfková, Ph.D. (11.05.2018)

Zápočet se uděluje za vypracování všech zadaných domácích úkolů a zároveň úspěšně napsané dva předem ohlášené zápočtové testy. Zápočtové testy lze opakovat ve dvou opravných termínech.

Zápočet JE NUTNOU PODMÍNKOU účasti u zkoušky.

Zkouška je ústní. Požadavky odpovídají sylabu předmětu v rozsahu, který byl prezentován na přednášce.

Literature - Czech
Last update: RNDr. Jitka Houfková, Ph.D. (11.05.2018)

Bílek O., Kapsa V.: Kvantová mechanika pro učitele, prozatímní skripta, dostupná

Skála, L. Úvod do kvantové mechaniky. 2. vyd. Praha: Academia, 2012.

Griffiths, D. J.: Introduction to Quantum Mechanics. Prentice Hall, Upper Saddle River. 1995

Pišút J., Gomolčák L., Černý V.: Úvod do kvantovej mechaniky. ALFA Bratislava-SNTL Praha 1983, dostupné online:

Blochincev D.I.: Základy kvantové mechaniky. NČSAV Praha 1956

Davydov A.S.: Kvantová mechanika. SPN Praha 1978

Klíma J., Velický B.: Kvantová mechanika I. Skriptum MFF UK, Praha 1992

Basdevant J.-L., Dalibard J.: Quantum mechanics Berlin : Springer, 2002

Brant, S.; Dahmen, H. D.; Stroh, T.: Interactive Quantum Mechanics. New York: Springer-Verlag, 2003.

Belloni, M.; Christian, W.; Cox, A. J.: Physlet Quantum Physics. An Interactive Introduction. Pearson, Prentice Hall, New Jersey, 2006.

Brandt S., Dahmen H. D.: The Picture Book of Quantum Mechanics. John Wiley and Sons, New York 1985

Styer D.F.: The Strange World of Quantum Mechanics, Cambridge University Press, Cambridge, 2000

Pišút J., Černý V., Prešnajder P.: Zbierka úloh z kvantovej mechaniky. ALFA Bratislava-SNTL Praha 1985

Teaching methods - Czech
Last update: T_KDF (12.05.2014)

integrovaná výuka - přednášky a cvičení se prolínají

Requirements to the exam - Czech
Last update: RNDr. Jitka Houfková, Ph.D. (11.05.2018)

Zápočet se uděluje za vypracování všech zadaných domácích úkolů a zároveň úspěšně napsané dva předem ohlášené zápočtové testy. Zápočtové testy lze opakovat ve dvou opravných termínech.

Zápočet JE NUTNOU PODMÍNKOU účasti u zkoušky.

Zkouška je ústní. Požadavky odpovídají sylabu předmětu v rozsahu, který byl prezentován na přednášce.

Syllabus -
Last update: T_KDF (12.05.2014)

(1) Introduction. The aim and scope of quantum mechanics (QM). Failure of classical physics as an origin of QM. Experiments leading to QM. Evolution of conceptions of microscopic particles and light. Characteristic features of microscopic systems: quantisation of physical observables, wave nature of particles, uncertainty relations, specificities of measurements in QM.

(2) Basic postulates and formalism of QM.

Description of quantum state. Wave function, its properties and interpretation. Normalization. Superposition principle, its interpretation and consequences. Vector space of quantum states. Scalar product.

Physical observables. Linear and hermitian operators. Operators of physical observables, its construction, correspondence principle. Commutation relations. Expectation values, eigenvalues and eigenfunctions of operators of physical observables.

Measurement in QM.

Schrödinger (nonstationary and stationary) equation. Continuity equation. Flux density. Time evolution and conservation laws. Energy levels. Integrals of motion. Quantum equations of motion. Ehrenfest theorems.

Relation between classical and quantum physics.

(3) Selected applications. Particle in rectangular potential box. Potential step. Potential barrier, tunnelling. Harmonic oscillator, atomic oscillation in crystals, normal modes. Free particle.

(4) Angular momentum. Particle in central field. Separation of coordinates and solution of multi-dimensional problems. Hydrogen atom.

(5) Spin. Experimental discovery of spin. Spin function. Spin operators. Pauli matrices. Pauli equation. Zeeman effect.

(6) Approximate methods of QM. Stationary perturbation theory for nondegenerate and degenerate energy levels. Nonstationary perturbation theory and quantum transitions. Variation methods. Selected applications.

(7) Many-particle systems. Extension of QM postulates for many-particle systems. Specificities of systems of identical particles. Indistinguishability principle and its consequences. Pauli principle. Periodic table. Adiabatic approximation, separation of electron and nuclear coordinates. Hydrogen atom as a two-particle problem. Helium.

(8) Chemical bond. Quantum explanation of chemical bond. Spin component of two particle wavefunction. Hydrogen molecule.

 
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