Geodesic
Asymptotic behavior of an~eigenvalue of the~two-particle discrete Schr\"odinger operator
Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 3, pp. 438-451

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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. 
@article{TMF_2012_171_3_a6,
     author = {S. N. Lakaev and A. M. Khalkhuzhaev and Sh. S. Lakaev},
     title = {Asymptotic behavior of an~eigenvalue of the~two-particle discrete {Schr\"odinger} operator},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {438--451},
     publisher = {mathdoc},
     volume = {171},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_171_3_a6/}
}
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S. N. Lakaev; A. M. Khalkhuzhaev; Sh. S. Lakaev. Asymptotic behavior of an~eigenvalue of the~two-particle discrete Schr\"odinger operator. Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 3, pp. 438-451. http://geodesic.mathdoc.fr/item/TMF_2012_171_3_a6/