Zh. I. Abdullaev, I. A. Ikromov, “Finiteness of the number of eigenvalues of the two-particle Schrödinger operator on a lattice”, TMF, 2007, Volume 152, Number 3,Pages <nobr>502

This article is cited in 13 papers

Finiteness of the number of eigenvalues of the two-particle Schrödinger operator on a lattice

Zh. I. Abdullaev, I. A. Ikromov

A. Navoi Samarkand State University

Abstract: We consider the two-particle Schrödinger operator $H(k)$ on the $\nu$-dimensional lattice $\mathbb{Z}^{\nu}$ and prove that the number of negative eigenvalues of $H(k)$ is finite for a wide class of potentials $\hat{v}$.

Keywords: Hamiltonian, Schrödinger operator, discrete spectrum, Birman–Schwinger principle.

Received: 19.06.2006
Revised: 02.12.2006

DOI: 10.4213/tmf6106