This article is cited in 7 papers

The number of eigenvalues of the two-particle discrete Schrödinger operator

S. N. Lakaev^a, A. M. Khalkhuzhaev<sup>b

a</sup> A. Navoi Samarkand State University
^b Uzbekistan Academy of Sciences, Samarkand Branch

Abstract: We consider the two-particle discrete Schrödinger operator associated with the Hamiltonian of a system of two particles (fermions) interacting only at the nearest neighbor sites. We find the number and the location of the eigenvalues of this operator depending on the particle interaction energy, the system quasimomentum, and the dimension of the lattice $\mathbb Z^\nu$, $\nu\ge1$.

Keywords: Hamiltonian, two-particle discrete Schrödinger operator, quasimomentum, essential spectrum, virtual level, eigenvalue, Fredholm determinant.

Received: 18.03.2008
Revised: 06.05.2008

DOI: 10.4213/tmf6313

 English version: Theoretical and Mathematical Physics, 2009, 158:2, 221–232

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