Geodesic
The number of eigenvalues of the two-particle discrete Schrödinger
Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 2, pp. 263-276 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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S. N. Lakaev; A. M. Khalkhuzhaev. The number of eigenvalues of the two-particle discrete Schrödinger. Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 2, pp. 263-276. http://geodesic.mathdoc.fr/item/TMF_2009_158_2_a6/

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