Advanced treatment of quantum theory, with an emphasis on the description and understanding of counterintuitive phenomena in quantum physics.
1. Basics: states and operators, unitary transformations, Heisenberg picture, equation of motion, uncertainty relation, pure states and mixtures, density matrix
2. Symmetry: conservation laws, unitary and anti-unitary symmetries, parity, time-reversal
3. Statistics: fermion and boson exchange, Fock space, second quantization, field operators
4. Variational principle: application to harmonic oscillator and helium, virial theorem
5. Semiclassics: Bohr-Sommerfeld quantization, WKB approximation, tunneling, level splitting
6. Time-dependent systems: evolution operator, time-ordering, adiabatic theorem, Landau-Zener transitions, Berry phase
7. Quantum particle in an electromagnetic field (a): gauge invariance, Aharonov-Bohm effect, flux quantization in superconductivity
Lectures, exercises, computer-assisted problems (Mathematica)
The course will follow closely the book: Quantum Mechanics: A New Introduction, by K. Konishi and G. Paffuti (Oxford University Press, 2009) [including a CD with Mathematica exercises, estimated paperback price €33]
Form of examination
Quantum Mechanics, Bachelor of Physics (Quantummechanica 1 and Quantummechanica 2)..