The hydrogen atom in $D=3-2ϵ$ dimensions

Abstract

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 $⟨(V^{\prime }{)}^2⟩$.

Comments: 5 pages