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On the evaluation of the norm of an integral operator associated with the stability of one-electron atoms. (English) Zbl 0917.47057

Summary: The norm of an integral operator occurring in the partial wave decomposition of an operator \(B\) introduced by Brown and Ravenhall in a model for relativistic one-electron atoms is determined. The result implies that \(B\) is nonnegative and has no eigenvalue at 0 when the nuclear charge does not exceed a specified critical value.

MSC:

47N50 Applications of operator theory in the physical sciences
47G10 Integral operators
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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References:

[1] Bethe, Handbuch der Physik, XXXV pp 88– (1957)
[2] DOI: 10.1112/S0024609397004256 · Zbl 0939.35134 · doi:10.1112/S0024609397004256
[3] DOI: 10.1098/rspa.1951.0181 · Zbl 0044.23209 · doi:10.1098/rspa.1951.0181
[4] DOI: 10.1007/BF02108822 · Zbl 0857.47041 · doi:10.1007/BF02108822
[5] DOI: 10.1103/PhysRevA.31.2020 · doi:10.1103/PhysRevA.31.2020
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