The hydrogen atom in $D=3-2\epsilon$ dimensions

Abstract

The nonrelativistic hydrogen atom in $D=3-2\epsilon$ 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 $\epsilon$. The utility of the series expansion is demonstrated by the calculation of the divergent expectation value $⟨(V^{\prime }{)}^2⟩$.

5 pages

References in corpus (2)

• Nonrelativistic QED approach to the Lamb shift
• Hydrogen atom in space with a compactified extra dimension and potential defined by Gauss' law

Cited by in corpus (3)

• Recoil corrections to the energy levels of hydrogenic atoms
• Coulomb expectation values in $D=3$ and $D=3-2\epsilon$ dimensions
• A generating integral for the matrix elements of the Coulomb Green's function with the Coulomb wave functions