Geodesic
Threshold phenomena in the~spectrum of the~two-particle Schr\"odinger operator on a~lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 198 (2019) no. 3, pp. 418-432

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For a broad class of short-range pairwise attraction potentials, we study threshold phenomena in the spectrum of the two-particle Schrödinger operator associated with the energy operator of the s–d exchange model. We prove that the bound state (eigenvalue) either exists or does not exist depending on the exchange interaction parameter, the system quasimomentum, and dimension of the lattice.
Keywords: discrete Schrödinger operator, two-particle system, energy operator, virtual level, eigenvalue, lattice.
Mots-clés : dispersion relation 
@article{TMF_2019_198_3_a2,
     author = {S. N. Lakaev and A. T. Boltaev},
     title = {Threshold phenomena in the~spectrum of the~two-particle {Schr\"odinger} operator on a~lattice},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {418--432},
     publisher = {mathdoc},
     volume = {198},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_198_3_a2/}
}
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S. N. Lakaev; A. T. Boltaev. Threshold phenomena in the~spectrum of the~two-particle Schr\"odinger operator on a~lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 198 (2019) no. 3, pp. 418-432. http://geodesic.mathdoc.fr/item/TMF_2019_198_3_a2/