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Quantum Theory


Admission Requirements

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


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 successful completion of the course you will 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.


Physics Schedule

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.)


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:

Prof.dr.Carlo Beenakker