On the discrete spectrum of the Hamiltonians of n-particle systems with n → ∞ in function spaces with various permutation symmetries

Abstract

The restrictions of the nonrelativistic energy operators H _n of the relative motion of a system of n identical particles with short-range interaction potentials to subspaces M of functions with various permutation symmetries are considered. It is proved that, for each of these restrictions, there exists an infinite increasing sequence of numbers N _j , j = 1, 2, …, such that the discrete spectrum of each operator $H_{N_j }$ on M is nonempty. The family {M} of considered subspaces is, apparently, close to maximal among those which can be handled by the existing methods of study.