Geodesic
Asymptotics of the Discrete Spectrum of the Three-Particle Schr\"odinger Difference Operator on a Lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 136 (2003) no. 2, pp. 231-245

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the Hamiltonian $H_\mu(K)$ of a system consisting of three bosons that interact through attractive pair contact potentials on a three-dimensional integer lattice. We obtain an asymptotic value for the number $N(K,z)$ of eigenvalues of the operator $H_{\mu_0}(K)$ lying below $z\le0$ with respect to the total quasimomentum $K\to0$ and the spectral parameter $z\to-0$.
Keywords: asymptotics, Schrödinger operator, essential spectrum, discrete spectrum, Hilbert–Schmidt operator. 
@article{TMF_2003_136_2_a3,
     author = {Zh. I. Abdullaev and S. N. Lakaev},
     title = {Asymptotics of the {Discrete} {Spectrum} of the {Three-Particle} {Schr\"odinger} {Difference} {Operator} on a {Lattice}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {231--245},
     publisher = {mathdoc},
     volume = {136},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2003_136_2_a3/}
}
TY  - JOUR
AU  - Zh. I. Abdullaev
AU  - S. N. Lakaev
TI  - Asymptotics of the Discrete Spectrum of the Three-Particle Schr\"odinger Difference Operator on a Lattice
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2003
SP  - 231
EP  - 245
VL  - 136
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2003_136_2_a3/
LA  - ru
ID  - TMF_2003_136_2_a3
ER  - 
%0 Journal Article
%A Zh. I. Abdullaev
%A S. N. Lakaev
%T Asymptotics of the Discrete Spectrum of the Three-Particle Schr\"odinger Difference Operator on a Lattice
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2003
%P 231-245
%V 136
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2003_136_2_a3/
%G ru
%F TMF_2003_136_2_a3
Zh. I. Abdullaev; S. N. Lakaev. Asymptotics of the Discrete Spectrum of the Three-Particle Schr\"odinger Difference Operator on a Lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 136 (2003) no. 2, pp. 231-245. http://geodesic.mathdoc.fr/item/TMF_2003_136_2_a3/