Modul: MAT675 PDE and Mathematical Physics

## On the spectrum of the Schrödinger operator on the d-dimensional torus: a normal form approach

Dr. Riccardo Montalto talk

Speaker invited by: Prof. Dr. Thomas Kappeler

**Date:** 07.11.19 **Time:** 18.10 - 19.10 **Room:** Y27H35/36

In this talk I will present a spectral result for the Schröodinger operator, perturbed with an unbounded potential of order strictly smaller than 2, on an arbitrary torus obtained as the quotient between R^d and a maximal d-dimensional lattice of R^d. I will show that it is possible to provide an asymptotic expansion of most of the eigenvalues of this operator. The proof is based on a "quantum normal form" involving pseudo differential operators and a standard "quasi-modes" argument. This is a joint work with Dario Bambusi and Beatrice Langella