Exact supersymmetry in the nonrelativistic hydrogen atom

We consider a Pauli particle in a Coulomb field. The supersymmetric Hamiltonian is constructed by explicitly giving the two supercharges ${\mathit{Q}}_1$ and ${\mathit{Q}}_2$ in the full three-dimensional space. These, 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.