Admission requirements
None.
Description
Advanced treatment of quantum theory, with an emphasis on the description and understanding of counterintuitive phenomena in quantum physics.
Topics:
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
Upon completion of this 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.
Schedule
The timetables are available through My Timetable (see the button in the upper right corner).
Teaching method
See Brightspace
Assesment method
The final grade will be determined as follows:
- Final exam (100%)
Resit, review & feedback
Examinations are held twice during the academic year for each component offered in that academic year. Midterm tests cannot be retaken. The Board of Examiners determines the manner of resit for practical assignments.
For review and feedback, see Brightspace.
Reading list
J.J. Sakurai, Modern Quantum Mechanics (third edition, 2022)
Registration
Enrolment through MyStudyMap (button in upper right corner) is mandatory. General information about course and exam enrolment is available on the website
Contact
For substantive questions, contact the lecturer(s) (listed in the right information bar).
Remarks
For additional course information see https://ilorentz.org/QT/