This article is cited in 25 papers

Asymptotic behavior of an eigenvalue of the two-particle discrete Schrödinger operator

S. N. Lakaev^ab, A. M. Khalkhuzhaev^ba, Sh. S. Lakaev<sup>b

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

Abstract: We consider a two-particle discrete Schrödinger operator corresponding to a system of two identical particles on a lattice interacting via an attractive pairwise zero-range potential. We show that there is a unique eigenvalue below the bottom of the essential spectrum for all values of the coupling constant and two-particle quasimomentum. We obtain a convergent expansion for the eigenvalue.

Keywords: Hamiltonian, discrete Schrödinger operator, quasimomentum, essential spectrum, eigenvalue, asymptotic expansion, eigenvalue expansion, Fredholm determinant.

Received: 24.08.2011

DOI: 10.4213/tmf6937

 English version: Theoretical and Mathematical Physics, 2012, 171:3, 800–811

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