|
This article is cited in 22 scientific papers (total in 22 papers)
Asymptotic behavior of an eigenvalue of the two-particle discrete Schrödinger operator
S. N. Lakaevab, A. M. Khalkhuzhaevba, Sh. S. Lakaevb a 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
Citation:
S. N. Lakaev, A. M. Khalkhuzhaev, Sh. S. Lakaev, “Asymptotic behavior of an eigenvalue of the two-particle discrete Schrödinger operator”, TMF, 171:3 (2012), 438–451; Theoret. and Math. Phys., 171:3 (2012), 800–811
Linking options:
https://www.mathnet.ru/eng/tmf6937https://doi.org/10.4213/tmf6937 https://www.mathnet.ru/eng/tmf/v171/i3/p438
|
Statistics & downloads: |
Abstract page: | 660 | Full-text PDF : | 244 | References: | 111 | First page: | 21 |
|