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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.

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

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.


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

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 information:

Prof.dr.Carlo Beenakker