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Spectral properties of a pseudorelativistic system of two particles with finite masses

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Abstract

The discrete spectrum of the Hamiltonian of a pseudorelativistic system of two particles with finite masses is investigated for a fixed total system momentum p and interaction potentials having the form Z|r12|−γ for large |r12|, where Z<0 and 0<γ≤2. The leading spectral asymptotic term is derived for γ<2. For γ=2, conditions are found for the finiteness and infiniteness of the discrete spectrum that depend (for some Z) on the fixed momentum p, which radically distinguishes the situation in question from the nonrelativistic case.

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Authors and Affiliations

  1. Research Institute for Radio Physics, Nizhnii Novgorod, Russia

    S. A. Vugal'ter & G. M. Zhislin

Authors
  1. S. A. Vugal'ter
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  2. G. M. Zhislin
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 121, No. 2, pp. 297–306, November, 1999.

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Vugal'ter, S.A., Zhislin, G.M. Spectral properties of a pseudorelativistic system of two particles with finite masses. Theor Math Phys 121, 1506–1515 (1999). https://doi.org/10.1007/BF02557221

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  • DOI: https://doi.org/10.1007/BF02557221

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