On the theory of the discrete spectrum of the three-particle Schr\"odinger operator

D. R. Yafaev

Sbornik. Mathematics, Tome 23 (1974) no. 4, pp. 535-559

Résumé

We investigate the discrete spectrum of the Schrödinger operator $H$ for a system of three particles. We assume that the operators $h_\alpha$, $\alpha=1,2,3$, which describe the three subsystems of two particles do not have any negative eigenvalues. Under the assumption that either two or three of the operators $h_\alpha$ have so-called virtual levels at the start of the continuous spectrum, we establish the existence of an infinite discrete spectrum for the three-particle operator $H$. The functions which describe the interactions between pairs of particles can be rapidly decreasing (or even of compact support) with respect to $x$. Bibliography: 17 titles.