## 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.

Basics: position and momentum representation, states and operators (bra-ket notation), unitary transformations, Heisenberg equations of motion, uncertainty relation, pure states and mixtures, density matrix

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

Time-independent quantum systems: theorems (virial, oscillation, variational, Ehrenfest, Hellmann-Feynman, Byers-Yang), Aharonov-Bohm effect, persistent current

Semiclassics: Bohr-Sommerfeld quantization, WKB approximation, resonant tunneling, Landau levels

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

Entanglement: EPR paradox, entanglement measures, Bell inequality, teleportation

Topology in condensed matter: Topological invariants, bulk-edge correspondence, Majorana modes, quantum Hall effect, quantum spin-Hall effect

## 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)

Computer assisted assignments ((week 1-5 of the online course at topocondmat.org )

## Assessment method

Part a: 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.)

Part b: oral presentation and computer assignments.

To pass for part b, a sufficient grade for part a is required.

## Blackboard

Course material is on Blackboard.

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

## Reading list

primary text book: L.E. Ballantine, Quantum Mechanics: A Modern Development

secondary text book: K. Konishi and G. Paffuti, Quantum Mechanics: A New Introduction

The second book is less detailed and systematic for the basics, but contains more applications. These books provide background and context to the material covered in the lectures and tutorials. In some cases, you will also find there alternative or more detailed derivations. While consulting these books is recommended, and is likely to help you understand and apply the material offered in the course, they also contain much additional material that goes beyond the course and will not be examinated.

## Contact

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