## Admission Requirements

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

## Description

Advanced treatment of quantum theory, with an emphasis on the description and understanding of counterintuitive phenomena in quantum physics.

*Fundamental concepts:* position and momentum representation, states and operators (bra-ket notation), unitary transformations, Heisenberg equations of motion, Ehrenfest theorem, Hellmann-Feynman theorem, uncertainty relation

*Symmetry:* conservation laws, unitary and anti-unitary symmetries, parity, time-reversal, Kramers degeneracy, Galilean invariance

*Fermions and bosons:* creation/annihilation operators, fermionic/bosonic Fock space, field operators, coherent states, Bogoliubov and Majorana quasiparticles in a superconductor

*Quantum electrodynamics:* gauge transformations, Byers-Yang theorem, Aharonov-Bohm effect, persistent current, Casimir effect

*Approximation methods:* variational methods, semiclassics, Bohr-Sommerfeld quantization, WKB approximation, applications to resonant tunneling and Landau level quantization

*Time-dependent quantum systems:* adiabatic theorem, Landau-Zener transitions, Berry phase, applications to Dirac fermions in graphene

*Path integrals:* Lagrangian, principle of least action, quantum propagator, Feynman path integral, stationary phase approximation

## Course objectives

After the course the student should be able to apply the basic concepts of quantum theory to macroscopic quantum phenomena, in particular in the context of quantum information processing and condensed matter physics. The emphasis is on a qualitative understanding of the general principles, rather than on specific computational techniques.

## Timetable

## Mode of instruction

Lectures + tutorials (exercise classes)

## Assessment method

Written examination, with questions modeled after the exercises from the tutorials. There is a possibility to retake the exam. (A date for the retake will be decided in consultation.)

## Blackboard

The course material can be accessed from Blackboard

To have access to Blackboard you need a ULCN-account.Blackboard UL

## Reading list

J.J. Sakurai, Modern Quantum Mechanics (second edition, 2017)

## Contact information:

Lecturers

Prof.dr.Carlo Beenakker