Discrete spectrum of a~noncompact perturbation of a~three-particle Schr\"odinger operator on a~lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 182 (2015) no. 3, pp. 435-452
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We consider a system of three arbitrary quantum particles on a three-dimensional lattice interacting via attractive pair-contact potentials and attractive potentials of particles at the nearest-neighbor sites. We prove that the Hamiltonian of the corresponding three-particle system has infinitely many eigenvalues. We also list different types of attractive potentials whose eigenvalues can be to the left of the essential spectrum, in a gap in the essential spectrum, and in the essential spectrum of the considered operator.
Keywords:
three-particle system on a lattice, Schrödinger operator, asymptotic number of eigenvalues, infinitely many eigenvalues in a gap in the essential spectrum, infinitely many eigenvalues in the essential spectrum.
@article{TMF_2015_182_3_a3,
author = {M. I. Muminov and N. M. Aliev},
title = {Discrete spectrum of a~noncompact perturbation of a~three-particle {Schr\"odinger} operator on a~lattice},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {435--452},
publisher = {mathdoc},
volume = {182},
number = {3},
year = {2015},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2015_182_3_a3/}
}
TY - JOUR AU - M. I. Muminov AU - N. M. Aliev TI - Discrete spectrum of a~noncompact perturbation of a~three-particle Schr\"odinger operator on a~lattice JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2015 SP - 435 EP - 452 VL - 182 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2015_182_3_a3/ LA - ru ID - TMF_2015_182_3_a3 ER -
%0 Journal Article %A M. I. Muminov %A N. M. Aliev %T Discrete spectrum of a~noncompact perturbation of a~three-particle Schr\"odinger operator on a~lattice %J Teoretičeskaâ i matematičeskaâ fizika %D 2015 %P 435-452 %V 182 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2015_182_3_a3/ %G ru %F TMF_2015_182_3_a3
M. I. Muminov; N. M. Aliev. Discrete spectrum of a~noncompact perturbation of a~three-particle Schr\"odinger operator on a~lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 182 (2015) no. 3, pp. 435-452. http://geodesic.mathdoc.fr/item/TMF_2015_182_3_a3/