QLunch: Lukas Schimmer

Speaker: Lukas Schimmer, Loughborough University, UK

Title: A Hardy inequality related to the optimal nucleus shape in relativistic quantum mechanics

Abstract: I will consider a quantum electron moving in the field of some (pointwise or extended) nuclei. In non-relativistic quantum mechanics, it is well known that the ground state energy is minimised when the nuclear charge is concentrated at one single point. In relativistic quantum mechanics, where the Schrödinger operator is replaced by the Dirac operator, this remains an open conjecture. I will discuss how the problem can be reformulated as a Hardy inequality and present some modest progress from ongoing work in this direction.