Quantum Mechanics 2
Code  Completion  Credits  Range 

02KVANM2  Z,ZK  6  4P+2C 
 Lecturer:
 Martin Štefaňák (guarantor)
 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:

Outline of the lecture:
1. Symmetries in quantum mechanics.
2. Tensor operators, WignerEckart 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. Nonstationary perturbation theory, timeordering 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.
Outline of the exercises:
1. Translations and rotations in quantum mechanics, parity, time inversion.
2. Addition of angular momenta, ClebschGordan coefficients, vector operators.
3. WignerEckart theorem, Lande’s gfactor, Stark’s effect for hydrogen.
4. Different pictures of quantum mechanics, particle in gravitational or magnetic field.
5. Density matrix of a twolevel 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 wavepacket.
11. Propagator of a free particle and linear harmonic oscillator via path integral.
12. Coulomb scattering.
13. Commutation and anticommutation relations for bosonic and fermionic creation and annihilation operators.
14. Free real KleinGordon’s field
 Syllabus of tutorials:

Outline of the exercises:
1. Translations and rotations in quantum mechanics, parity, time inversion.
2. Addition of angular momenta, ClebschGordan coefficients, vector operators.
3. WignerEckart theorem, Lande’s gfactor, Stark’s effect for hydrogen.
4. Different pictures of quantum mechanics, particle in gravitational or magnetic field.
5. Density matrix of a twolevel 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 wavepacket.
11. Propagator of a free particle and linear harmonic oscillator via path integral.
12. Coulomb scattering.
13. Commutation and anticommutation relations for bosonic and fermionic creation and annihilation operators.
14. Free real KleinGordon’s field
 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] A. Hoskovec, J. Lochman: Zápisky z kvantové mechaniky 2, elektronická skripta FJFI, 2018. (in czech)
(available at https://physics.fjfi.cvut.cz/files/predmety/02KVAN2/02KVAN2)
[2] J. Formánek: Úvod do kvantové teorie I, II, Academia, Praha 2004. (in czech)
Recommended references:
[3] D. J. Griffiths, Introduction to Quantum Mechanics, Cambridge University Press, 2016.
[4] C. CohenTannoudji, B. Diu, F. Laloe: Quantum Mechanics. WileyVCH, 1992.
[5] L. H. Ryder, Quantum Field Theory, Cambridge University Press, Cambridge 1996.
[6] L. D. Faddeev and O. A. Yakubovskii: Lectures on Quantum Mechanics for Mathematics Students (Student Mathematical Library), AMS 2009.
[7] A. Messiah, Quantum Mechanics, Two Volumes Bound as One, (Dover Publications, New York, 1999).
[8] P.A.M. Dirac, Principles of Quantum Mechanics, Oxford University Press, Oxford 1958.
 Note:
 Timetable for winter semester 2019/2020:
 Timetable is not available yet
 Timetable for summer semester 2019/2020:
 Timetable is not available yet
 The course is a part of the following study plans: