Exact supersymmetry in the nonrelativistic hydrogen atom

TL;DR

This paper constructs a supersymmetric Hamiltonian for a Pauli particle in a Coulomb field, revealing an $S(2)$ superalgebra structure that groups energy states into symmetry representations.

Contribution

It explicitly formulates supercharges and demonstrates the supersymmetry algebra in a nonrelativistic hydrogen atom model.

Findings

Supercharges $Q_1$ and $Q_2$ are explicitly constructed.

The Hamiltonian forms an $S(2)$ superalgebra.

Energy eigenstates are grouped into irreducible representations.

Abstract

We consider a Pauli particle in a Coulomb field. The supersymmetric Hamiltonian is constructed, by explicitly giving the two supercharges $Q_{1}$ and $ Q_{2}$ in the full three-dimensional space and which together with the Hamiltonian, are shown to constitute an $S(2)$ superalgebra. This offers an alternative way of grouping the energy eigenstates into irreducible representations of this symmetry group of the Hamiltonian.