V3B2 SoSe 2017 - Mathematical Institute of the University of Bonn

RG Analysis and Partial Differential Equations

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: