Quantum Mechanics 2
Code  Completion  Credits  Range  Language 

02KVA2B  Z,ZK  6  4+2  Czech 
 Course guarantor:
 Lecturer:
 Tutor:
 Supervisor:
 Department of Physics
 Synopsis:

Symmetry in quantum mechanics, invariance and conservation laws, approximate methods, scattering theory, systems of identical particles
 Requirements:

Knowledge of the basic course of physics and subject 02KVAN  Quantum mechanics
 Syllabus of lectures:

1. Symmetry: general formalism, continuous and discrete transformations, generators. Translation, rotation.
2. Parity, time inversion. Gauge transformation, particle in an electromagnetic field.
3. Addition of angular momenta: ClebschGordan coefficients , 6jsymbols, Irreducible tensor operators, WignerEckart theorem.
4. Elementary theory of representations: Energy, coordinate and momentum representations, General properties of solutions of Schroedinger equation, Free particle solution, decomposition of the plane wave into partial waves.
5. Time evolution and propagators: Schroedinger, Heisenberg and Dirac pictures, Resolvent, stationary Green function, Propagator, retarded a advanced Green operator, LippmannSchwinger equation and perturbative solution for the evolution operator
6. Approximate methods: Variational method, helium atom. WKB method, connection formulas, tunneling.
7. Timedependent perturbation theory, various perturbations, Fermi golden rule. Transitions between discrete levels and into continuum, particle scattered by an external field.
8. Particle in e.m. field: Pauli equation, photoeffect.
9. Introduction into scattering theory: From timedependent to timeindependent description, Wave operators, Smatrix and Tmatrix, Stationary scattering states, LippmannSchwinger equation, scattering amplitude and cross section.
10. Born series, partial waves, phase shifts. Solutions in coordinate and momentum representations.
11. Systems of identical particles: Pauli principle, (anti)symmetrization of wave functions. Oneparticle basis, Slater determinants,
12. Fock space, creation and annihilation operators, one and twoparticle operators, HartreeFock method.
 Syllabus of tutorials:

1. Symmetry:
general formalism, continuous and discrete transformations, generators. Translation, rotation.
2. Parity, time inversion.
Gauge transformation, particle in an electromagnetic field.
3. Addition of angular momenta: ClebschGordan coefficients , 6jsymbols, irreducible tensor operators, WignerEckart theorem.
4. Elementary theory of representations:
Energy, coordinate and momentum representations, General properties of solutions of Schroedinger equation, Free particle solution, decomposition of the plane wave into partial waves.
5. Time evolution and propagators: Schroedinger, Heisenberg and Dirac pictures, Resolvent, stationary Green function, Propagator, retarded a advanced Green operator, LippmannSchwinger equation and perturbative solution for the evolution operator
6. Approximate methods:
Variational method, helium atom. WKB method, connection formulas, tunneling.
7. Timedependent perturbation theory, various perturbations, Fermi golden rule. Transitions between discrete levels and into continuum, particle scattered by an external field.
8. Particle in e.m. field: Pauli equation, photoeffect.
9. Introduction into scattering theory:
From timedependent to timeindependent description, Wave operators, Smatrix and Tmatrix, Stationary scattering states, LippmannSchwinger equation, scattering amplitude and cross section.
10. Born series, partial waves, phase shifts. Solutions in coordinate and momentum representations.
11. Systems of identical particles:
Pauli principle, (anti)symmetrization of wave functions.
Oneparticle basis, Slater determinants,
12. Fock space, creation and annihilation operators, one and twoparticle operators, HartreeFock method.
 Study Objective:

Knowledge:
Advanced quantummechanical methods, perturbative formulation and second quantization
Abilities:
Application of quantum description and various (in particular perturbative) methods of solution on realistic microscopic systems
 Study materials:

Key references:
[1] D.J. Griffiths: Introduction to Quantum Mechanics, Prentice Hall, 2nd edition, 2004
[2] J. Formánek: Introduction in Quentum mechanics I,II, Academia, 2004 (in Czech)
Recommended references:
[3] J.R. Taylor: Scattering Theory, J. Wiley and Sons, 1972
[4] E. Merzbacher: Quantum Mechanics, 3rd edition, John Wiley, 1998
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans: