Geodesic
The~number of eigenvalues of the~two-particle discrete Schr\"odinger
Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 2, pp. 263-276

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We consider the two-particle discrete Schrödinger operator associated with the Hamiltonian of a system of two particles (fermions) interacting only at the nearest neighbor sites. We find the number and the location of the eigenvalues of this operator depending on the particle interaction energy, the system quasimomentum, and the dimension of the lattice $\mathbb Z^\nu$, $\nu\ge1$.
Keywords: Hamiltonian, two-particle discrete Schrödinger operator, quasimomentum, essential spectrum, virtual level, eigenvalue, Fredholm determinant. 
@article{TMF_2009_158_2_a6,
     author = {S. N. Lakaev and A. M. Khalkhuzhaev},
     title = {The~number of eigenvalues of the~two-particle discrete {Schr\"odinger}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {263--276},
     publisher = {mathdoc},
     volume = {158},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_158_2_a6/}
}
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S. N. Lakaev; A. M. Khalkhuzhaev. The~number of eigenvalues of the~two-particle discrete Schr\"odinger. Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 2, pp. 263-276. http://geodesic.mathdoc.fr/item/TMF_2009_158_2_a6/