Quantum Mechanics 1

Garant předmětu:

Craig Hamilton

Lecturer:

Craig Hamilton

Tutor:

Craig Hamilton

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:

Basic knowledge of classical mechanics, electromagnetism, theoretical physics, waves and optics, calculus and linear algebra.

Syllabus of lectures:

1. Experiments leading to the birth of QM

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

3. Description of states and observables in QM

4. Elements of Hilbert space theory and operators

5. Measurement in quantum mechanics, transition probabilities

6. Spin-1/2 particle

7. Linear harmonic oscillator

8. Quantization of angular momentum

9. Particle in a spherical potential – isotropic oscillator, Coulomb field

10. Position and momentum

11. Mean values of observables and transition probabilities, uncertainty relations

12. Time evolution of states

Syllabus of tutorials:

1. Summary of classical hamiltonian mechanics, statistical physics and probability theory

2. De Broglie waves

3. Particle in an infinite square well, spin-1/2 particle

4. Linear harmonic oscillator

5. Orbital angular momentum

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

7. Time evolution in quantum mechanics

8. Free particle, spreading of the wave-packet

Study Objective:

Study materials:

Key references:

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

Recommended references:

[2] L. D. Faddeev and O. A. Yakubovskii: Lectures on Quantum Mechanics for Mathematics Students (Student Mathematical Library), AMS 2009.

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

Note:

Time-table for winter semester 2023/2024:

Time-table is not available yet

Time-table for summer semester 2023/2024:

Time-table is not available yet

The course is a part of the following study plans: