## Description

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

## Programme form

Lectures, exercises, computer-assisted problems (Mathematica)

## Literature

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]

## Schedule

## Form of examination

Written exam

## Prerequisites

Quantum Mechanics, Bachelor of Physics (Quantummechanica 1 and Quantummechanica 2).

## More information

Lecturer: Prof.dr.C.Beenakker(Carlo)