G. M. Zhislin, “On the discrete spectrum of the Hamiltonians of $n$-particle systems with $n\to\infty$ in function spaces with various permutation symmetries”, Funktsional. Anal. i Prilozhen., 2015, Volume 49, Issue 2,Pages 85

This article is cited in 1 paper

Brief communications

On the discrete spectrum of the Hamiltonians of $n$-particle systems with $n\to\infty$ in function spaces with various permutation symmetries

G. M. Zhislin^ab

^a N. I. Lobachevski State University of Nizhni Novgorod
^b Scientific Research Institute of Radio Physics, Nizhnii Novgorod

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 $N_j$, $j=1,2,\dots$, 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.

Keywords: many-particle Hamiltonian, discrete spectrum, permutation symmetry.

UDC: 519.4

Received: 11.09.2013

DOI: 10.4213/faa3189