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The spectrum of relativistic one-electron atoms according to Bethe and Salpeter. (English) Zbl 0857.47041

Summary: Bethe and Salpeter introduced a relativistic equation – different from the Bethe-Salpeter equation – which describes relativistic multi-particle systems. Here we will begin some basic work concerning its mathematical structure. In particular we show selfadjointness of the one-particle operator which will be a consequence of a sharp Sobolev type inequality yielding semi-boundedness of the corresponding sesquilinear form. Moreover we locate the essential spectrum of the operator and show the absence of singular continuous spectrum.

MSC:

47N50 Applications of operator theory in the physical sciences
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81Q40 Bethe-Salpeter and other integral equations arising in quantum theory
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