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Course: Quantum Mechanics 2

Department/Abbreviation: SLO/KM2X

Year: 2020

Guarantee: 'Mgr. Jiří Kvita, Ph.D.', 'prof. RNDr. Jan Peřina, Ph.D.'

Annotation: Principles of quantum mechanics.

Course review:
1. Time-dependent perturbation theory a. Harmonic perturbation 2. Statistical operator, Liouville equation, density matrix, pure and mixed states. 3. Lagrangian and Hamiltonian of a particle in electromagnetic field, Landau levels, spinless particle, Pauli equation, calibration invariance. 4. Spin revisited a. Magnetic resonance b. Addition of spins, singlet and triplet states, baryons and mesons 5. Identical particles a. Permutations, spin and statistics, fermions and bosons b. Covalent bond, ortho and para hydrogen c. Fock states, second quantization, creation and annihilation operators. 6. Symmetries, generators of translations and rotations. 7. Crystals, solid state, band structure a. Bloch waves b. Brilloune zones 8. Evolution in time revisited a. Hamiltonian as generator of time translations, evolution operator b. Free particle propagator, Green functions c. Schrödinger and Heisenberg pictures, Dirac picture 9. Simple scattering theory a. Lippmann-Schwinger equation b. Scattering amplitude, cross-section c. Born series, Coulomb and Yukawa potentials d. Optical theorem 10. Dirac equation a. Derivation, bispinors, gamma matrices, Dirac algebra b. Basic properties and solutions