Geodesic
The number of bound states of a one-particle Hamiltonian on a three-dimensional lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 3, pp. 425-443 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the Hamiltonian $\hat h_{\mu\lambda}$, $\mu,\lambda\ge0$, describing the motion of one quantum particle on a three-dimensional lattice in an external field. We investigate the number of eigenvalues and their arrangement depending on the value of the interaction energy for $\mu\ge0$ and $\lambda\ge0$.
Keywords: one-particle Hamiltonian, continuous spectrum, virtual level, eigenvalue, Birman—Schwinger operator, Fredholm determinant. 
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S. N. Lakaev; I. N. Bozorov. The number of bound states of a one-particle Hamiltonian on a three-dimensional lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 3, pp. 425-443. http://geodesic.mathdoc.fr/item/TMF_2009_158_3_a8/

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