Which nuclear shape generates the strongest attraction on a relativistic electron? An open problem in relativistic quantum mechanics
Analysis of PDEs
2023-11-06 v2 Mathematical Physics
math.MP
Spectral Theory
Abstract
In this article we formulate several conjectures concerning the lowest eigenvalue of a Dirac operator with an external electrostatic potential. The latter describes a relativistic quantum electron moving in the field of some (pointwise or extended) nuclei. The main question we ask is whether the eigenvalue is minimal when the nuclear charge is concentrated at one single point. This well-known property in nonrelativistic quantum mechanics has escaped all attempts of proof in the relativistic case.
Keywords
Cite
@article{arxiv.2203.13484,
title = {Which nuclear shape generates the strongest attraction on a relativistic electron? An open problem in relativistic quantum mechanics},
author = {Maria J. Esteban and Mathieu Lewin and Eric Séré},
journal= {arXiv preprint arXiv:2203.13484},
year = {2023}
}
Comments
Mathematics Going Forward, In press