Geodesic
Spectral properties of a pseudorelativistic system of two particles with finite masses
Teoretičeskaâ i matematičeskaâ fizika, Tome 121 (1999) no. 2, pp. 297-306 
S. A. Vugal'ter; G. M. Zhislin. Spectral properties of a pseudorelativistic system of two particles with finite masses. Teoretičeskaâ i matematičeskaâ fizika, Tome 121 (1999) no. 2, pp. 297-306. http://geodesic.mathdoc.fr/item/TMF_1999_121_2_a6/
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     title = {Spectral properties of a pseudorelativistic system of two particles with finite masses},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_121_2_a6/}
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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 $Z|r_{12}|^{-\gamma}$ for large $|r_{12}|$, where $Z<0$ and $0<\gamma\leq2$. The leading spectral asymptotic term is derived for $\gamma<2$. For $\gamma=2$, 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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