Code: 02KVA2B 
Quantum Mechanics 2 
Lecturer: prom. fyz. Jiří Adam CSc. 
Weekly load: 4+2 
Completion: A, EX 
Department: 14102 
Credits: 6 
Semester: S 
 Description:

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

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.
 Recommended literature:

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
 Keywords:
 Quantum mechanics, harmonic oscillator, symmetry, perturbation theory
Abbreviations used:
Semester:
 W ... winter semester (usually October  February)
 S ... spring semester (usually March  June)
 W,S ... both semesters
Mode of completion of the course:
 A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
 GA ... Graded Assessment (a grade is awarded for this course)
 EX ... Examination
 A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject)