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

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dc.creatorBrummelhuis, Raymond
dc.creatorRuskai, Mary Beth
dc.creatorWerner, Elisabeth
dc.date1999-12-28
dc.date.accessioned2026-07-07T04:33:09Z
dc.date.available2026-07-07T04:33:09Z
dc.descriptionWe 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.
dc.description9 pages, Proceedings of a conference on Differential Equations and Mathematical Physics at University of Alabama Birmingham (March 1998)
dc.identifierhttps://arxiv.org/abs/math-ph/9912020
dc.identifierhttp://arxiv.org/abs/math-ph/9912020
dc.identifierDifferential Equations and Mathematical Physics, ed. by G. Weinstein and R. Weikard, pp. 43-51 (International Press, 2000)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58466
dc.subjectMathematical Physics
dc.subjectClassical Analysis and ODEs
dc.subjectAtomic Physics
dc.subject81V45, 33E20
dc.titleOne Dimensional Regularizations of the Coulomb Potential with Application to Atoms in Strong Magnetic Fields
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