### Abstract

We show how the Schrödinger 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)⋉R2. We show that the solutions of the Schrödinger equation may be organized into an algebraic family of Harish-Chandra modules. Furthermore, we use Jantzen filtration techniques to algebraically recover the spectrum of the Schrödinger operator. This is a first application to physics of the algebraic families of Harish-Chandra pairs and modules developed in the work of Bernstein et al. [Int. Math. Res. Notices, rny147 (2018); rny146 (2018)].

Original language | English (US) |
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Article number | 071702 |

Journal | Journal of Mathematical Physics |

Volume | 59 |

Issue number | 7 |

DOIs | |

State | Published - Jul 1 2018 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics