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

被引：0

作者：

S. N. Lakaev

A. M. Khalkhuzhaev

Sh. S. Lakaev

机构：

[1] Uzbekistan Academy of Sciences,Samarkand Branch

[2] Samarkand State University,undefined

来源：

Theoretical and Mathematical Physics | 2012年 / 171卷

关键词：

Hamiltonian; discrete Schrödinger operator; quasimomentum; essential spectrum; eigenvalue; asymptotic expansion; eigenvalue expansion; Fredholm determinant;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

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页码：800 / 811

页数：11

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