The hydrogen atom in D = 3 − 2ϵ dimensions

The nonrelativistic hydrogen atom in D=3−2ϵ dimensions is the reference system for perturbative schemes used in dimensionally regularized nonrelativistic effective field theories to describe hydrogen-like atoms. Solutions to the D-dimensional Schrödinger-Coulomb equation are given in the form of a double power series. Energies and normalization integrals are obtained numerically and also perturbatively in terms of ϵ. The utility of the series expansion is demonstrated by the calculation of the divergent expectation value 〈(V′)2〉.