Course Contents
The course is divided in four blocks (each of them consisting of roughly 5 to 6 lectures):
1) Fundamentals of quantum mechanics, time-dependent and time-independent perturbation theory, Fermi's golden rule
2) Scattering theory, partial waves, Born approximation
3) Many-body quantum physics, Bose and Fermi statistics
4) Relativistic quantum mechanics, Dirac equation
First class is a general introduction to the lecture, motivating the relevance of each topic presented.
After each block, there will be a review lecture, highlighting the main results derived.
At the end of the lecture, there will be a general review and concluding class.
[b]Here is the detailed list of lectures: [/b]
1. Quantum operators and states. The Schrödinger equation
2. Heisenberg and interaction pictures. The quantum harmonic oscillator. The particle in a box.
3. The hydrogen atom - review of main aspects
4. Time independent perturbation theory
5. Spin-orbit coupling. Time dependent perturbation theory. Fermi’s golden rule.
6. Review
7. Lippmann-Schwinger theory and the Born expansion
8. Scattering amplitudes and cross-sections. The Born approximation for spherically symmetric potentials.
9. Partial waves, phase shifts and the optical theorem
10. Review
11. Introducing many body physics problems
12. Creation/annihilation and field operators
13. The H[sup]+[/sup][sub]2[/sub] molecule
14. The Helium atom
15. The Hubbard model
16. Magnetism. The Heisenberg and Ising models
17. Review
18. Special relativity. The Dirac equations
19. Relativistic quantum mechanics - The Dirac equation
20. The Klein paradox. Lagrangian and stationary action
21. Quantum electrodynamics
22. Final review
Preconditions
Course in Theoretical Physics:
Mechanics, Electrodynamics,Quantum Mechanics.
- Lecturer: Claudiu Genes