Physics – Mathematical Physics
Scientific paper
1999-12-28
Differential Equations and Mathematical Physics, ed. by G. Weinstein and R. Weikard, pp. 43-51 (International Press, 2000)
Physics
Mathematical Physics
9 pages, Proceedings of a conference on Differential Equations and Mathematical Physics at University of Alabama Birmingham (M
Scientific paper
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.
Brummelhuis Raymond
Ruskai Mary Beth
Werner Elisabeth
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