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: Clebsch-Gordan coefficients , 6j-symbols, Irreducible tensor operators, Wigner-Eckart 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, Lippmann-Schwinger equation and perturbative solution for the evolution operator
6. Approximate methods: Variational method, helium atom. WKB method, connection formulas, tunneling.
7. Time-dependent 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 time-dependent to time-independent description, Wave operators, S-matrix and T-matrix, Stationary scattering states, Lippmann-Schwinger 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. One-particle basis, Slater determinants,
12. Fock space, creation and annihilation operators, one- and two-particle operators, Hartree-Fock 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

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