Quantum mechanics is one of the subjects in physics that has influenced Mathematics during the last century. For example, it has drastically influenced the development of Functional Analysis, Spectral Theory and Operator Theory.

Goal of this lecture series is to discuss how to investigate Quantum Mechanics from a mathematically rigorous point of view. This makes course having a different aspects than Quantum Mechanics courses from the Physics point of view. Contents include observable and self-adjointness (which requires more than what usually physicists consider as self-adjoint) , existence of dynamics of Schrödinger equations, spectral properties of Schödinger operators, the uncertainty principle, existence and stability of atoms. Note that the course will have a second part in summer semester and in the second part we will also cover some topics of actual research.

Prerequisites: Analysis, linear Algebra. It is recommended that you have taken functional analysis or that you take it parallel to the class. If you are not sure about your background please talk to me.

# Summaries of the lectures

Posting of brief summaries of the lectures is planned to be done till Sunday afternoon of the weak before them. This file give a very dry text having only the notation, definitions and theorems, without any proofs, examples, remarks or motivation. The purpose of this is that you get the possibility to see a little bit what will come in the next week each time. It is highly recommended that you read it and think about it even for a short of time before coming to the lecture. Such a small effort from your side might make you understand much more during the lecture than you would understand without any preparation. The file will be updated every week. If you find any typos please send an email to ioannis.anapolitanos@kit.edu, so that they get corrected.

Summaries of lectures

# Lecture notes

In the following link you find informal lecture notes for the course. Some additional small explanations given in the lecture might not always be here but the most important parts are written here.

The other way around too, some staff that we did not have enough time to go thoughroully during the lecture might be explained in a more detail in the notes. If you find any typos please send an email to ioannis.anapolitanos@kit.edu

http://www.math.kit.edu/iana1/lehre/quantummech2019w/seite/lecturenotes/

# Exercise sheets

In the following link you can find the exercise sheets

http://www.math.kit.edu/iana1/lehre/quantummech2019w/seite/exercises/

# Feedback for the course

Your feedback for the course (suggestions, difficulties, critisism) is highly appreciated. You can either talk to us, or if you are too shy to do this, you can anonymously write in the following link.

https://docs.google.com/forms/d/e/1FAIpQLSejNtsQRe4oEa5HUxjubs6UOT5f3CRkUnnd-d8I__9TOzS_-A/viewform?usp=send_form

# Examination

**There is going to be an oral exam for the course**

# References

1. Gustavson S., Sigal I.M.: Mathematical Concepts of Quantum mechanics third edition Springer 2011

2. Reed M., Simon B.: Methods of Modern Mathematical Physics Volumes I-IV, Academic Press

3. Berezin F.A. , Shubin M.A.: The Schödinger Equation. Kluwer Academic Publishers 1991.