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Quantum mechanics of electromagnetically bounded spin-1/2 particles in expanding universes: II. Energy spectrum of the hydrogen atom

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Abstract

Completing the preceding paper, the energy spectrum of the hydrogen atom in expanding Robertson-Walker universes is studied in detail using rigorous methods of functional analysis. Thereby, for closed universes (spherical case,ε=1), the corresponding electromagnetic field needs special considerations. For the hyperbolic case (ε=−1) it is shown (a) that the Hamilton operator is uniquely self-adjoint, (b) that the continuous energy spectrum agrees with the one in 4-flat space-time and that the energy eigenvalues are bounded by±m 0 , (c) that they approach Minkowski space spectrum for increasing curvature radius, and (d) that the hydrogen atom cannot be used as an atomic clock showing proper time. For the spherical case (ε=1) it is shown (a) that the Hamilton operator is uniquely self-adjoint and (b) that the energy spectrum is solely discrete.

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Authors and Affiliations

  1. Fachbereich Physik der Universität Konstanz, Postfach 7733, D-7750, Konstanz, West Germany

    J. Audretsch & G. Schäfer

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  1. J. Audretsch
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  2. G. Schäfer
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Audretsch, J., Schäfer, G. Quantum mechanics of electromagnetically bounded spin-1/2 particles in expanding universes: II. Energy spectrum of the hydrogen atom. Gen Relat Gravit 9, 489–500 (1978). https://doi.org/10.1007/BF00759543

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