Families of Symmetries and the Hydrogen Atom
Abstract
We study a new type of symmetry for the hydrogen atom involving algebraic families of groups parametrized by the energy value in the time-independent Schr\"odinger equation. We construct an algebraic family of Harish-Chandra modules from the solutions of the Schr\"odinger equation, and we characterize this family. We show that the subspaces of physical states may be obtained from our algebraic family using a Jantzen filtration, and we relate our algebraic methods with spectral theory and scattering theory using the limiting absorption principle
Keywords
Cite
@article{arxiv.1908.01905,
title = {Families of Symmetries and the Hydrogen Atom},
author = {Nigel Higson and Eyal Subag},
journal= {arXiv preprint arXiv:1908.01905},
year = {2022}
}
Comments
Following the advice of the anonymous referee the title was changed and the introduction was revised. A new paragraph commenting on the dynamical symmetry O(4,2) and its minimal representation was added