Quantum Mechanics 1

Garant předmětu:

Martin Štefaňák

Lecturer:

Martin Štefaňák

Tutor:

Tereza Lehečková, Magdalena Parýzková, Stanislav Skoupý, Martin Štefaňák

Supervisor:

Department of Physics

Synopsis:

Abstract:

The lecture describes the birth of quantum mechanics and description of one particle and more particles by elements of the Hilbert space as well as its time evolution. Besides that it includes description of observable quantities by operators in the Hilbert space and calculation of their spectra.

Requirements:

Prerequisites for completing the course 02TEF1.

Syllabus of lectures:

Outline of the lecture:

1. Experiments leading to the birth of QM

2. De Broglie's conjecture, Schroedinger's equation

3. Description of states in QM

4. Elements of Hilbert space theory and operators

5. Harmonic oscillator

6. Quantization of angular momentum

7. Particle in the Coulomb field

8. Mean values of observables and transition probabilities

9. Time evolution of states

10. Particle in the electromagnetic field. Spin

11. Perturbation methods

12. Many particle systems

13. Potential scattering, tunneling phenomenon

Syllabus of tutorials:

Outline of the exercises:

Solving problems to illustrate the theory from the lecture.

Study Objective:

Knowledge:

Knowledge and understanding of fundamental principles of quantum mechanics - description of states and observables, interference of probability amplitudes, role of measurement on the quantum state, transition probability, time evolution of a closed system.

Abilities:

Application of principles of quantum mechanics in basic models (spin, free particle, linear harmonic oscillator, hydrogen atom). Ability to determine probabilities of measurement outcomes and average values of observables. Solving the Schroedinger equation by decomposition into the basis of energy eigenstates.

Study materials:

Key references:

[1] D. J. Griffiths, Introduction to Quantum Mechanics, Cambridge University Press, 2016.

[2] C. Cohen-Tannoudji, B. Diu, F. Laloe: Quantum Mechanics. Wiley-VCH, 1992

[3] K. Gottfried, T. Yan: Quantum mechanics: Fundamentals, Springer, 2013.

[4] N. Zettili: Quantum Mechanics: Concepts and Applications, Wiley; 2nd edition, 2009.

Recommended references:

[5] A. Messiah, Quantum Mechanics, Two Volumes Bound as One, (Dover Publications, New York, 1999).

[6] P.A.M. Dirac, Principles of Quantum Mechanics, Oxford University Press, Oxford 1958.

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Fyzikální inženýrství - Počítačová fyzika (PS)
• Aplikovaná algebra a analýza (compulsory course in the program)
• Fyzikální inženýrství - Inženýrství pevných látek (PS)
• Jaderná a částicová fyzika (compulsory course in the program)
• Fyzikální inženýrství - Laserová technika a fotonika (PS)
• Matematické inženýrství - Matematická fyzika (PS)
• Kvantové technologie (compulsory course in the program)
• Physical Engineering - Computational physics (PS)
• Quantum Technologies (compulsory course in the program)
• Nuclear and Particle Physics (compulsory course in the program)