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One Dimensional Regularizations of the Coulomb Potential with Application to Atoms in Strong Magnetic Fields

Raymond Brummelhuis·Mary Beth Ruskai·Elisabeth Werner
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Abstract

We consider one-dimensional regularizations of the Coulomb potential formed by taking a two-dimensional expectation of the Coulomb potential with respect to the Landau states. It is well-known that such functions arises naturally in the study of atoms in strong magnetic fields. For many-electron atoms consideration of the Pauli principle requires convex combinations of such potentials and interactions in which the regularizations also contain a 2^{-1/2} rescaling. We summarize the results of a comprehensive study of these functions including recursion relations, tight bounds, convexity properties, and connections with confluent hypergeometric functions. We also report briefly on their application in one-dimensional models of many-electrons atoms in strong magnetic fields.

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Raymond Brummelhuis, Mary Beth Ruskai, Elisabeth Werner. 1999-12-28. One Dimensional Regularizations of the Coulomb Potential with Application to Atoms in Strong Magnetic Fields. https://arxiv.org/abs/math-ph/9912020

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