Geodesic
Finiteness of the~number of eigenvalues of the~two-particle Schr\"odinger operator on a~lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 3, pp. 502-517

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We consider the two-particle Schrödinger operator $H(k)$ on the $\nu$-dimensional lattice $\mathbb{Z}^{\nu}$ and prove that the number of negative eigenvalues of $H(k)$ is finite for a wide class of potentials $\hat{v}$.
Keywords: Hamiltonian, Schrödinger operator, discrete spectrum, Birman–Schwinger principle. 
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     author = {Zh. I. Abdullaev and I. A. Ikromov},
     title = {Finiteness of the~number of eigenvalues of the~two-particle {Schr\"odinger} operator on a~lattice},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {152},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_152_3_a7/}
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Zh. I. Abdullaev; I. A. Ikromov. Finiteness of the~number of eigenvalues of the~two-particle Schr\"odinger operator on a~lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 3, pp. 502-517. http://geodesic.mathdoc.fr/item/TMF_2007_152_3_a7/