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Mathematical Aspects of Quantum Mechanics (University of Zurich)
Last Updated: 2026-02-05 16:02:14
Abstract
The course aims at presenting the basic theory of Quantum Mechanics from the mathematical point of view.No prior knowledge of Quantum Mechanics is required, and the language and tools necessary to develop the theory will be explicitly introduced.
Objective
After the course students should have learned topics of spectral theory for unbounded operators and the description of simple models of one- particle quantum systems.
Content
We will start with the main mathematical tools of QM: the theory of Hilbert spaces and unbounded operators, self-adjoint and unitary operators, and the spectral theorem. The standard axiomatic description of Quantum Mechanics, main motivation behind the above topics, will also be presented and discussed. This will be followed by the analysis of simple models of one-particle systems such as the free particle, the harmonic oscillator, and the hydrogen atom. Further topics as conservation laws and the angular momentum operators will also be discussed. If time permits, we will also touch more advanced topics, as for example the theory of general Schrödinger operators and the semiclassical approximation.
Resources
Literature
• Lecture note written by Benjamin Schlein for the course MAT631 Mathematical Aspects of Quantum Mechanics for the Spring Semester 2018 • Schmüdgen – Unbounded Self-adjoint Operators on Hilbert Space • Teta - A Mathematical Primer on Quantum Mechanics
General Information
- Language
- English
- Levels
- BSC , MSC
Examination
- Type
- graded semester performance
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Mathematical Aspects of Quantum Mechanics (University of Zurich) | No time listed | 4 h weekly |
Offered In
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Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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