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Fachbereich Mathematik


Benutzerspezifische Werkzeuge

Foundations of Quantum Mechanics

Current updates: No class on Friday 9 Feb 2018.

Course Language:

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

Math: Multivariable calculus 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, held also by Prof. Tumulka. 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.

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)
Foundations of Quantum Mechanics


Prof. Dr. Roderich Tumulka





Lecture Notes

Homework assignments