Algebraic Solution of the Supersymmetric Hydrogen Atom
The N=2 supersymmetric extension of the Schrödinger-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.
hep-th↗