Symmetries of the hydrogen atom and algebraic families

@article{Subag2017SymmetriesOT,
  title={Symmetries of the hydrogen atom and algebraic families},
  author={Eyal M. Subag},
  journal={Journal of Mathematical Physics},
  year={2017}
}
  • E. Subag
  • Published 21 October 2017
  • Mathematics
  • Journal of Mathematical Physics
We show how the Schrodinger equation for the hydrogen atom in two dimensions gives rise to an algebraic family of Harish-Chandra pairs that codifies hidden symmetries. The hidden symmetries vary continuously between $SO(3)$, $SO(2,1)$ and the Euclidean group $O(2)\ltimes \mathbb{R}^2$. We show that solutions of the Schrodinger equation may be organized into an algebraic family of Harish-Chandra modules. Furthermore, we use Jantzen filtration techniques to algebraically recover the spectrum of… 

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