Families of Symmetries and the Hydrogen Atom
arXiv:1908.01905 · doi:10.1016/j.aim.2022.108586
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 Schrödinger equation. We construct an algebraic family of Harish-Chandra modules from the solutions of the Schrödinger 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
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