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Canonical partition function for the hydrogen atom in curved space

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Abstract

The electronic partition function for the hydrogen atom was recently derived by integration over the Coulomb propagator. A much simpler derivation is given here, based on Schrödinger's exact solution for a hydrogenic atom in a Riemannian space of positive curvature. The energy spectrum is entirely discrete, including states which correspond to the ionized atom. The curvature in Riemannian space is shown to be equivalent to a finite volume in Euclidean space.

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References

  1. S.M. Blinder, J. Math. Phys. 36 (1995) 1208. This paper contains references to earlier work on the hydrogen partition function.

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  2. E. Schrödinger, Proc. Irish Acad. A46 (1940) 9; see also: N. Bessis and G. Bessis, J. Phys. A. Math. Gen. 12 (1979) 1991.

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Authors and Affiliations

  1. Department of Chemistry, University of Michigan, M148109-1055, Ann Arbor, USA

    S. M. Blinder

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  1. S. M. Blinder
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Blinder, S.M. Canonical partition function for the hydrogen atom in curved space. J Math Chem 19, 43–46 (1996). https://doi.org/10.1007/BF01165129

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  • DOI: https://doi.org/10.1007/BF01165129

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