Quantum Mechanics 2

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Physics

Synopsis:

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:

Syllabus of lectures:

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 operator.

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:

1. Translations and rotations in quantum mechanics, parity, time inversion.

2. Addition of angular momenta, Clebsch-Gordan coefficients, vector operators.

3. Wigner-Eckart theorem, Lande’s g-factor, Stark’s effect for hydrogen.

4. Different pictures of quantum mechanics, particle in gravitational or magnetic field.

5. Density matrix of a two-level system, thermal state of a harmonic oscillator, Gibbs state.

6. JWKB approximation of an infinite potential well, linear harmonic oscillator, tunneling.

7. Ritz variation method for a helium atom.

8. Model of an interaction of the electromagnetic field EM with matter.

9. Sudden change of Hamiltonian, infinite potential well, tritium decay.

10. Propagator of a free particle, spreading of the wave-packet.

11. Propagator of a free particle and linear harmonic oscillator via path integral.

12. Coulomb scattering.

13. Commutation and anti-commutation relations for bosonic and fermionic creation and annihilation opera

Study Objective:

Knowledge:

Introduction to more advanced topics in quantum mechanics.

Acquired skills:

Application of general formalism of quantum theory, approximation methods and path integral.

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, 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: