Algebraic Solution of the Supersymmetric Hydrogen Atom in d Dimensions
A. Kirchberg, J.D. Laenge, P.A.G. Pisani, A. Wipf
TL;DR
This paper constructs the N=2 supersymmetric extension of the hydrogen atom Hamiltonian in arbitrary dimensions, revealing hidden symmetries that determine eigenvalues, degeneracies, and wave functions.
Contribution
It introduces a supersymmetric framework for the hydrogen atom in any dimension, uncovering hidden symmetries and explicitly solving for eigenvalues and wave functions.
Findings
Identifies a conserved Laplace-Runge-Lenz vector in supersymmetric hydrogen
Reveals hidden SO(d+1) symmetry in the system
Determines discrete eigenvalues and degeneracies
Abstract
In this paper the N=2 supersymmetric extension of the Schroedinger Hamiltonian with 1/r-potential in arbitrary space-dimensions is constructed. The supersymmetric hydrogen atom admits a conserved Laplace-Runge-Lenz vector which extends the rotational symmetry SO(d) to a hidden SO(d+1) symmetry. This symmetry of the system is used to determine the discrete eigenvalues with their degeneracies and the corresponding bound state wave functions.
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