Quantum Mechanics 2

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Physics

Synopsis:

Abstract:

The lecture expands the introduction to quantum mechanics with more general formalism of quantum theory, approximate methods and path integral. It summarizes the terminology and methods used in various applications of quantum mechanics and prepares the students for an effective scientific research and further study, in particular, of the modern formulations of quantum field theory.

Requirements:

Prerequisites for completing the course 02TEF2.

Syllabus of lectures:

Outline of the lecture:

1. Symmetries in quantum mechanics.

2. Tensor operators, Wigner-Eckart theorem.

3. Different representations of quantum mechanics, Heisenberg’s and Dirac’s picture.

4. Density matrix, entanglement, mixed states, master equation.

5. Wigner–Weyl transformation, Moyal bracket, deformation quantization, Wigner function.

6. JWKB approximation, Ritz variation method.

7. Jump and adiabatic change of the Hamiltonian.

8. Non-stationary perturbation theory, time-ordering operatoration.

9. Propagator, Green’s function, partition sum in quantum mechanics.

10. Path integral in quantum mechanics.

11. Perturbation expansion of path integral, Feynman’s diagrams.

12. Description of scattering with path integral.

13. Indistinguishable particles, annihilation and creation operators, Fock’s space.

14. Brief introduction to quantum field theory.

Syllabus of tutorials:

Outline of the exercises:

Solving problems to illustrate the theory from the lecture.

Study Objective:

Knowledge:

Knowledge of advanced parts of quantum theorie, with focus on symmetries and perturbative methods for solving stationary and non-stationary problems, and their application in more involved models (fine structure of hydrogen, anomalous Zeeman effect, Stark effect). Basics of scattering theory, quantization of fields and interaction of a quantum particle with a quantized electromagnetic field.

Abilities:

Use of symmetries for evaluation of matrix elements. Description of a quantum state with a density matrix. Energy estimation via variational and WKB methods. Determination of transition rates in 1st order non-stationary perturbation theory for a constant and harmonic perturbation. Description of bosons and fermions in a Fock space.

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

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

Recommended references:

[5] L. H. Ryder, Quantum Field Theory, Cambridge University Press, Cambridge 1996.

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

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

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