Arbeitsgruppe Analysis und Partielle Differentialgleichungen


V3B2 - PDG und Modellierung, PDE and Modelling (Sommersemester 2017/ Summer term 2017):

Mathematical concepts of quantum mechanics



Instructor: Prof. Dr. Herbert Koch
Assistant: Dr. Xian Liao


Time and Place:

    Wednesday, 10 (c.t.) - 12 am, Zeichensaal (Wegelerstr. 10)
    Friday, 08 (c.t.) - 10 am, Zeichensaal (Wegelerstr. 10)

Office hours:

    Friday, 10 - 11 am, by appointment

Contents:

    Fourier transform, unbounded selfadjoint operators, Stones theorem on unitary semigroups, the spectrum of selfadjoint operator. What is quantum behavior? Wave and particle behaviour. Schrödinger operator and wave functions. The uncertainty principle. Free particle, harmonic oscillator, and hydrogen atom. Scattering. Many particle systems and density matrices.
Required and recommended background:

    Functional analysis of Hilbert spaces, Lebesgue spaces, Distributions.

References (Textbooks):

  • R.P. Feynman & R.B. Leighton & M. Sands, The Feynman lectures on physics, Vol. 3: Quantum mechanics. Addison-Wesley 1965.
  • S. Gustafson & I.M. Sigal, Mathematical concepts of quantum mechanics. Springer 2006.
  • R. Penrose, The road to reality: A complete guide to the laws of the universe. Alfred A. Knopf 2005.
  • B. Simon, Operator theory. AMS 2016.
  • G. Teschl, Mathematical methods in quantum mechanics: With applications to Schrödinger operators. AMS 2014.
  • S. Weinberg, Lectures in quantum mechanics. Cambridge 2013.

Tutorials:

Time Room Tutor
Tuesday 4-6 pm SemR 0.007 Jonas Jansen
Thursday 10-12 am SemR 0.007 Florian Schweiger
Notes:


Exercise Sheets:


1st oral examination:

    Friday, 28. July 2017 and Thursday, 03. August 2017.
2nd oral examination:

    Monday, 11. September 2017.