Algebraic Solution of the Supersymmetric Hydrogen Atom
A. Wipf, A. Kirchberg, J.D. L\"ange
TL;DR
This paper constructs an N=2 supersymmetric extension of the hydrogen atom in arbitrary dimensions, revealing hidden symmetries and explicitly solving for eigenvalues and wave functions.
Contribution
It introduces a supersymmetric framework for the hydrogen atom, extending symmetries and providing explicit solutions for eigenvalues and wave functions.
Findings
Identifies a supersymmetrized Laplace-Runge-Lenz vector
Reveals hidden SO(d+1) symmetry
Determines eigenvalues and bound state wave functions
Abstract
The N=2 supersymmetric extension of the Schr\"odinger-Hamiltonian with 1/r-potential in d dimension is constructed. The system admits a supersymmetrized Laplace-Runge-Lenz vector which extends the rotational SO(d) symmetry to a hidden SO(d+1) symmetry. It is used to determine the discrete eigenvalues with their degeneracies and the corresponding bound state wave functions.
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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Quantum and Classical Electrodynamics · Quantum chaos and dynamical systems