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：
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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.
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页码：800 / 811
页数：11
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