Geodesic
On compact distribution of two-particle Schr\"odinger operator on a~lattice
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2015), pp. 24-30

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We consider a system of two arbitrary quantum particles on three-dimensional lattice with certain dispersion functions (they describe a transfer of a particle from one node to another) which with the help of gravity potential interact on nearest neighboring nodes, only. We find a class of potentials such that under perturbation of two-particle operator $h(k)$, which corresponds to a system of two particles with a potential from this class, a discrete operator $h(k)$ is kept.
Keywords: two-particle Hamiltonian on a lattice, virtual level, multiplicity of virtual level, eigenvalue, discrete spectrum. 
@article{IVM_2015_6_a3,
     author = {M. I. Muminov and A. M. Khurramov},
     title = {On compact distribution of two-particle {Schr\"odinger} operator on a~lattice},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {24--30},
     publisher = {mathdoc},
     number = {6},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_6_a3/}
}
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M. I. Muminov; A. M. Khurramov. On compact distribution of two-particle Schr\"odinger operator on a~lattice. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2015), pp. 24-30. http://geodesic.mathdoc.fr/item/IVM_2015_6_a3/