Niels Benedikter

Teaching assistant, IST Austria 2018

Teaching assistant for the course "Stability of Matter in Quantum Mechanics" with Prof. Robert Seiringer.

Research into the stability of matter has been one of the most successful chapters in mathematical physics, and is a prime example of how modern mathematics can be applied to problems in physics. This course provides a self-contained description of research on the stability of matter problem. It introduces the necessary aspects of functional analysis as well as the quantum mechanical background. The topics covered include Lieb-Thirring and other inequalities in spectral theory, inequalities in electrostatics, stability of large Coulomb systems, and gravitational stability of stars.

Advanced Mathematical Physics, Copenhagen 2017
  • July 6: Seminar notes "Van der Waals Force" available. You can pick up your corrected assignments in office 04.2.11 until July 14.

Lecture Notes:

Lectures Niels:

Lectures Jérémy:

Assignments (to be handed in at the beginning of the Friday seminar!):

Summer School on Current Topics in Mathematic Physics at the University of Zurich, Switzerland, July 17 - July 21:

Seminar: All talks have to be about 40 minutes long (not more!). Schedule is subject to changes depending on our progression in the lecture. The summary is due on Monday after the seminar. Please remember to provide a list of references. Contact Jérémy or me at least two weeks before your talk for a briefing. Topics and summaries:

Criteria for passing the course:
Reach approximately 50% of the points averaged over the four assignments.
Give a seminar talk and produce a summary of your talk for the other participants.

Literature: The lecture notes should be self-contained for most of the course. If you are looking for additional reading, here are some recommendations.

  • Gerald Teschl: Mathematical Methods in Quantum Mechanics. Online version

    Contains essentially all topics of the lecture, but in a different arrangement. Sometimes details are missing.

  • Stephen J. Gustafson, Israel Michael Sigal: Mathematical Concepts of Quantum Mechanics. Online version

    Nice selection of material, but sometimes sketchy. Good overview.

  • Michael Reed, Barry Simon: Methods of Modern Mathematical Physics, Volumes I-IV.

    Recommended as a reference work, not as a text book. Concise but rather dense.

  • Elliott H. Lieb, Michael Loss: Analysis. Errata

    A functional analysis book aimed at applications in quantum mechanics. Contains many useful explicit estimates.

If you want to read up on quantum mechanics from the physicist point of view (which is not the focus of this course):

  • Gordon Baym: Lectures on Quantum Mechanics
  • Leslie E. Ballentine: Quantum Mechanics, A Modern Development
  • Steven Weinberg: Lectures on Quantum Mechanics
Advanced Mathematical Physics, Copenhagen 2016

Thank you all for following the course! New materials for the 2017 course will appear above.

Teaching assistant, Bonn 2011-2014

I assisted Prof. Benjamin Schlein at the University of Bonn for the courses

and for a Summer School at the University of Heidelberg