Spectral estimates for Schrödinger operators and the stability of matter

Specialeforsvar: Mia Megan Fox

Titel: Spectral estimates for Schrödinger operators and the stability of matter

Abstract: 
In this project, we show the stability of matter of a quantum mechanical many-body system with N electrons and M nuclei. We first prove the Lieb-Thirring inequality, which is used to control the kinetic energy of the particles, and then proceed to show why it holds in our system. Afterwards, we prove the stability of matter of the first kind by disregarding the positive contributions to the Coulomb potential energy and reducing the problem to a single-body problem. Before we show the stability of matter of the second kind, we prove two electrostatic inequalities that again allow us to reduce it to a single-body problem, while this time keeping part of the positive contribution to the Coulomb potential. By doing this, the proof of stability of matter of the second kind is simplified and proceeds relatively simply, like the proof of stability of the first kind.

Vejleder: Jan Philip Solovej
Censor: Michael Pedersen, DTU