  We employ our new approach to non-relativistic supersymmetric quantum
mechanics (SUSY-QM), (J. Phys. Chem. A 114, 8202(2010)) for any number of
dimensions and distinguishable particles, to treat the hydrogen atom in full
three-dimensional detail. In contrast to the standard one-dimensional radial
equation SUSY-QM treatment of the hydrogen atom, where the superpotential is a
scalar, in a full three-dimensional treatment, it is a vector which applies
regardless of the electron angular momentum. The original scalar Schrodinger
Hamiltonian operator is factored into vector "charge" operators: Q and
Q^{dagger}. Using these operators, the first sector Hamiltonian is written as
H1 = Q^{\dagger} * Q. The second sector Hamiltonian is a tensor given by H2 = Q
Q^{\dagger} and is isospectral with H1. The second sector ground state,
psi^{(2)}_0, can be used to obtain the excited state wave functions of the
first sector by application of the adjoint charge operator. Alternatively, Q
applied to analytical, sector one excited states yield analytical results for
the sector two vector eigenstates. Several of these are plotted for
illustration. We then adapt the aufbau principle to show this approach can be
applied to treat the helium atom.

Quantum Physics;Chemical Physics