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arXiv · 1801.02191

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

Gregory S. Adkins
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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 $\langle (V')^2 \rangle$.

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Gregory S. Adkins. 2018-01-07. The hydrogen atom in $D=3-2ε$ dimensions. https://doi.org/10.1016/j.physleta.2018.03.048

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