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

S. A. Vugal'ter ; G. M. Zhislin

Teoretičeskaâ i matematičeskaâ fizika, Tome 121 (1999) no. 2, pp. 297-306

Résumé

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 $Z0$ and $0\gamma\leq2$. The leading spectral asymptotic term is derived for $\gamma2$. 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.