Universität Regensburg   IMPRESSUM   DATENSCHUTZ
Fakultät für Mathematik Universität Regensburg
Schrödinger operators
Semester
WiSe 2022 / 23

Lecturer
Bernd Ammann, Gunnar Bali (Physik)

Type of course (Veranstaltungsart)
Seminar

German title
Schrödinger-Operatoren

Contents
In this seminar we want to study the Schrödinger operator -Δ+V(x) as a densely defined differential operator from L2(ℝ3) to L2(ℝ3), mainly concerned with the Coulomb potential V(x)=-c/||x||. We are also interested in generalizations and in connections to representation theory. In particular, this leads to a good understanding of the orbital model in physics and chemistry.

In order to study this subject we have to start with foundations in functional analysis, with a focus on the aspects needed for Schrödinger operators. We will discuss self-adjoint extensions, discrete and essential spectra, the characterization of the essential spectrum in terms of Weyl sequences. As the potential is unbounded, eigenfunctions are in general not smooth. We show that eigenfunctions are bounded, and discuss their (higher) differentiability. Generalisations we have in mind are the multi-electron Schrödinger equations and Dirac operators with Coulomb type potentials. The seminar will mainly follow the book by Teschl cited below, with some additional talks at the end.

Literature
Main reference:

Other literature
  • H. L. Cycon, R.g. Froese, W. Kirsch, B. Simon, Schrödinger Operators (with applicatiosn to Quantum Mechanics and Global Geometry)
  • Michael Reed and Barry Simon, Methods of modern mathematical physics, Vol. I-V
  • Dirk Werner, Funktionalanalysis, Springer
  • Hans Wilhelm Alt, Lineare Funktionalanalysis, Springer
  • Siegfried Großmann, Funktionalanalysis (im Hinblick auf Anwendungen in der Physik), AULA-Verlag
  • Bernd Thaller, The Dirac equation, Springer
  • Gernot Münster: Quantentheorie Direct Link, available from the UR campus or with VPN
  • Chris J. Isham: Lectures on Quantum Theory


Recommended previous knowledge
Dieses Seminar richtiet sich vor allem an Studierende ab dem 5. Semester mit Interesse an Mathematik und Physik

Time/Date
see webpage

Location
see webpage

Course homepage
https://ammann.app.uni-regensburg.de/lehre/2022w_schroedinger
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration
  • Organisational meeting/distribution of topics: Wednesday 27.7. at 16:15 in PHY 4.1.12
    (Physik)<br> You may follow via Zoom, access data on GRIPS
  • Bitte auch in GRIPS registrieren. Link zur GRIPS-Seite auf der Webseite
  • Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)
  • Presentation: Giving a seminar talk of roughly 90 minutes
Examination (Prüfungsleistungen)
  • Detailed written report of the seminar talk
Additional comments
Alle Teilnehmer können zB im Dezemeber wählen, ob sie die ECTS-Punkte für ein
Mathematik- oder ein Physik-Seminar erhalten wollen

Modules
BSem, MV, MSem, noch zu klärende Physik-Module

ECTS
4,5