Bound states of the~Schr\"odinger operator of a~system of three bosons on a~lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 1, pp. 36-48
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We consider the Hamiltonian $H_\mu$ of a system of three identical quantum particles (bosons) moving on a $d$-dimensional lattice $\mathbb Z^d$, $d=1,2$, and coupled by an attractive pairwise contact potential $\mu0$. We prove that the number of bound states of the corresponding Schrödinger operator $H_\mu(K)$, $K\in\mathbb T^d$, is finite and establish the location and structure of its essential spectrum. We show that the bound state decays exponentially at infinity and that the eigenvalue and the corresponding bound state as functions of the quasimomentum $K\in\mathbb T^d$ are regular.
Keywords:
discrete Schrodinger operator, three-particle system, contact coupling,
eigenvalue, bound state, essential spectrum, lattice.
@article{TMF_2016_188_1_a2,
author = {S. N. Lakaev and A. R. Khalmukhamedov and A. M. Khalkhuzhaev},
title = {Bound states of {the~Schr\"odinger} operator of a~system of three bosons on a~lattice},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {36--48},
publisher = {mathdoc},
volume = {188},
number = {1},
year = {2016},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2016_188_1_a2/}
}
TY - JOUR AU - S. N. Lakaev AU - A. R. Khalmukhamedov AU - A. M. Khalkhuzhaev TI - Bound states of the~Schr\"odinger operator of a~system of three bosons on a~lattice JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2016 SP - 36 EP - 48 VL - 188 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2016_188_1_a2/ LA - ru ID - TMF_2016_188_1_a2 ER -
%0 Journal Article %A S. N. Lakaev %A A. R. Khalmukhamedov %A A. M. Khalkhuzhaev %T Bound states of the~Schr\"odinger operator of a~system of three bosons on a~lattice %J Teoretičeskaâ i matematičeskaâ fizika %D 2016 %P 36-48 %V 188 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2016_188_1_a2/ %G ru %F TMF_2016_188_1_a2
S. N. Lakaev; A. R. Khalmukhamedov; A. M. Khalkhuzhaev. Bound states of the~Schr\"odinger operator of a~system of three bosons on a~lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 1, pp. 36-48. http://geodesic.mathdoc.fr/item/TMF_2016_188_1_a2/