Geodesic
The~number of bound states of a~one-particle Hamiltonian on a~three-dimensional lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 3, pp. 425-443

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

We consider the Hamiltonian $\hat h_{\mu\lambda}$, $\mu,\lambda\ge0$, describing the motion of one quantum particle on a three-dimensional lattice in an external field. We investigate the number of eigenvalues and their arrangement depending on the value of the interaction energy for $\mu\ge0$ and $\lambda\ge0$.
Keywords: one-particle Hamiltonian, continuous spectrum, virtual level, eigenvalue, Birman—Schwinger operator, Fredholm determinant. 
@article{TMF_2009_158_3_a8,
     author = {S. N. Lakaev and I. N. Bozorov},
     title = {The~number of bound states of a~one-particle {Hamiltonian} on a~three-dimensional lattice},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {425--443},
     publisher = {mathdoc},
     volume = {158},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_158_3_a8/}
}
TY  - JOUR
AU  - S. N. Lakaev
AU  - I. N. Bozorov
TI  - The~number of bound states of a~one-particle Hamiltonian on a~three-dimensional lattice
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2009
SP  - 425
EP  - 443
VL  - 158
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2009_158_3_a8/
LA  - ru
ID  - TMF_2009_158_3_a8
ER  - 
%0 Journal Article
%A S. N. Lakaev
%A I. N. Bozorov
%T The~number of bound states of a~one-particle Hamiltonian on a~three-dimensional lattice
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2009
%P 425-443
%V 158
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2009_158_3_a8/
%G ru
%F TMF_2009_158_3_a8
S. N. Lakaev; I. N. Bozorov. The~number of bound states of a~one-particle Hamiltonian on a~three-dimensional lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 3, pp. 425-443. http://geodesic.mathdoc.fr/item/TMF_2009_158_3_a8/