Fachbereich Mathematik

Foundations of Quantum Mechanics

Practice exam

Exams will be oral exams (20 minutes). Please contact Mrs. Kabagema-Bilan for scheduling and registering your exam.

Conditions for onsite participation:
3G rule (geimpft, genesen oder getestet). That is, you can participate in the classroom only if (a) you are free from Covid symptoms and (b) you can show documentation that you are either fully vaccinated or recovered or tested negatively (within the previous 24 hours by an antigen quick test or within the previous 48 hours by a PCR test). Do-it-yourself-tests will not be accepted. For more details see here.

Lecture notes:

How students rated this course:
Results of evaluation questionnaire (December 2021)

Course language:

This course is offered particularly for the Master in Mathematical Physics Program but is open to all degree programs.

Math: Multivariable calculus (Analysis 2) and linear algebra.
Physics: Prior knowledge is helpful but not required.

It has been claimed that quantum mechanics entails most radical consequences about the world and our knowledge of it, such as the existence of parallel universes, faster-than-light action-at-a-distance, limitations to what we can know, that reality itself be paradoxical, or that electrons become real only when observed. On the other hand, it has been claimed that quantum mechanics, in its orthodox formulation, be "unprofessional" (J. Bell), "incoherent" (A. Einstein), "incomprehensible" (R. Feynman), and "insane" (E. Schrödinger). We will investigate these claims, their basis and merits. The course will involve advanced mathematics, as appropriate for a serious discussion of quantum mechanics, but will not focus on technical methods of problem-solving. This course, intended for physics and math students, focuses on what can be concluded from quantum mechanics about the nature of reality.

Topics will include most of the following: The Schrödinger equation, the Born rule, self-adjoint matrices, axioms of the quantum formalism, the double-slit experiment, non-locality and Bell’s theorem, the paradox of Schrödinger's cat, the quantum measurement problem, Heisenberg's uncertainty relation, interpretations of quantum mechanics (Copenhagen, Bohm's trajectories, Everett's many worlds, spontaneous collapse theories, quantum logic, perhaps others), views of Bohr and Einstein, the Einstein-Podolsky-Rosen argument, no-hidden-variables theorems, and identical particles.

Learning goals:
To understand the rules of quantum mechanics; to understand several important views of how the quantum world works; to understand what is controversial about the orthodox interpretation and why; to be familiar with the surprising phenomena and paradoxes of quantum mechanics.

The two weekly 90-minute lectures are accompanied by one weekly 90-minute exercise class. The weekly homework assignment will comprise math problems, essay questions, and reading assignments (3-8 pages per week). Participants need to register on the URM website for the exercises.

ECTS credits:
9 points

Online or on campus?
If the pandemic situation permits, the classes will be taught on campus (in lecture hall N14, C building, level 3). Simultaneously, the class will be accessible online via zoom, and lectures will be recorded, so it will also be possible to participate online. For participation on campus, the number of seats will be limited, and if the demand exceeds that number then we will take turns.

Course grade:
will be based on an oral exam.

The instructor provides his lecture notes and weekly reading assignments.
Additional suggestions:

  • J. S. Bell: Speakable and Unspeakable in Quantum Mechanics, 2nd ed. Cambridge University Press (2004)
  • J. Bricmont: Making Sense of Quantum Mechanics. Springer-Verlag (2016)
  • T. Norsen: Foundations of Quantum Mechanics. Springer-Verlag (2017)

Further reading for math students: