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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 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
For detailed information go to Timetable in Brightspace

You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have sucessfully registered for in MyStudyMap will automatically be displayed in MyTimeTable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.

MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).

For more information, watch the video or go the the 'help-page' in MyTimetable. Please note: Joint Degree students Leiden/Delft have to merge their two different timetables into one. This video explains how to do this.

Mode of instruction

see Brightspace

Assessment method

Written examination, with questions modeled after the exercises from the tutorials. There is a possibility to retake the exam.

Reading list

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


From the academic year 2022-2023 on every student has to register for courses with the new enrollment tool MyStudyMap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December. Please see this page for more information.

Please note that it is compulsory to both preregister and confirm your participation for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course. Confirming your exam participation is possible until ten days before the exam.

Extensive FAQ's on MyStudymap can be found here.


Lecturer: Prof.dr. C.W.J. Beenakker


For additional course information, see