Seminar (Functional Analysis): Random and Almost Periodic Schrödinger Operators
Wintersemester 2013/14

Time and Place
Type: Time: Place: Start:
PJSE 2 std. Do 11:30-13:00 SR10 3.10
Random and almost periodic Schrödinger operators serve in solid state physics as models of disordered systems such as alloys, glasses and amorphous materials in the so called tight binding approximation. In quantum mechanics, crystals are modeled by Schrödinger operators with periodic potentials. It is an important problem to understand what happens to a crystal if random impurities are introduced. Indeed, in a more realistic setting such crystals will contain impurities, the precise locations of which are in general unknown. All one might know is that these impurities occur with a certain probability. During the last three decades, random Schrödinger operators became an extremely extensive topic and much effort has been put to understand the properties of random and almost periodic operators. Our main aim is to shed some light on a circle of ideas and problems and to the mathematical machinery that has recently been built to investigate it.
Date: Title: Speaker: References:
10.10Introduction: Why random Schrödinger operatorsGerald Teschl[Ki]
24.10Discrete Schrödinger operators and spectral calculusMarkus Holzleitner[Ki]
31.10Random potentialsTobias Schubhart[Ki]
07.11Ergodic operatorsDamir Ferizović[Ki]
14.11The density of states: Definitions and existenceFranz Berger[Ki]
21.11The density of states: The geometric resolvent equationMelanie Graf[Ki]
28.11The Wegner estimateOliver Skocek[Ki]
12.12Lifshitz tailsNoema Nicolussi[Ki]
23.01The spectrum and its physical interpretationZouhair Hadded[Ki]


  1. J. Bourgain, Green's Function Estimates for Lattice Schrödinger Operators and Applications, Princeton UP, 2005.
  2. H. L. Cycon, R. G. Froese, W. Kirsch, and B. Simon, Schrödinger Operators, 2nd ed., Springer, 2008.
  3. W. Kirsch, An invitation to random Schrödinger operators, in: Panor. Syntheses, 25, Random Schrödinger operators, 1-119, 2008.
  4. A. Klein, Multiscale analysis and localization of random operators, in: Panor. Syntheses, 25, Random Schrödinger operators, 121-159, 2008.
  5. G. Teschl, Jacobi Operators and Completely Integrable Nonlinear Lattices, AMS, 2000.
Course assessment
Preparation and presentation of a chosen topic.
Majors in Mathematics (master program, code MANS), Physics, ...
Auf Ihr Kommen freuen sich Aleksey Kostenko und Gerald Teschl