Quantum Mechanics

Garant předmětu:

Martin Štefaňák

Lecturer:

Martin Štefaňák

Tutor:

Stanislav Skoupý, Martin Štefaňák, Daniel Štěrba

Supervisor:

Department of Physics

Synopsis:

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:

Absolutely necessary is good knowledge of hamiltonian formulation of classical mechanics, linear algebra including operation on infinitely dimensional spaces, calculus in several variables and Fourier analysis. Contact lecturer before inscription.

Syllabus of lectures:

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:

1. Summary of classical hamiltonian mechanics and statistical physics

2. De Broglie waves

3. Free particle, spreading of the wave-packet

4. Particle in a finite and infinite square well

5. Linear harmonic oscillator

6. Orbital angular momentum

7. Ladder operators

8. Predictions of measurement outcomes, mean values of observables, uncertainty relations

9. Time evolution in quantum mechanics

10. Spin of the electron, algebraic theory of angular momentum, composition of two independent angular momenta

11. Perturbation theory

Study Objective:

knowledge:

The goal of the lecture is to explain fundamentals and mathematical methods of the quantum mechanics.

abilities:

apply mathematical methods to problems of quantum mechanics

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:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: