Geodesic
Conditions for the existence of bound states of a two-particle Hamiltonian on a three-dimensional lattice
Nanosistemy: fizika, himiâ, matematika, Tome 13 (2022) no. 3, pp. 237-244.

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

The Hamiltonian h of the system of two quantum particles moving on a 3-dimensional lattice interacting via some attractive potential is considered. Conditions for the existence of eigenvalues of the two-particle Schrödinger operator $h_{\mu}(k)$, $k\in\mathbb T^{3}$, $\mu\in\mathbb R$, associated to the Hamiltonian h, are studied depending on the energy of the particle interaction $\mu\in\mathbb R$ and total quasi-momentum $k\in\mathbb T^{3}$ ($\mathbb T^{3}$ – three-dimensional torus).
Keywords: two-particle Hamiltonian, invariant subspace, unitary equivalent operator, virtual level, multiplicity of virtual level, eigenvalue. 
@article{NANO_2022_13_3_a0,
     author = {M. I. Muminov and A. M. Khurramov and I. N. Bozorov},
     title = {Conditions for the existence of bound states of a two-particle {Hamiltonian} on a three-dimensional lattice},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {237--244},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2022_13_3_a0/}
}
TY  - JOUR
AU  - M. I. Muminov
AU  - A. M. Khurramov
AU  - I. N. Bozorov
TI  - Conditions for the existence of bound states of a two-particle Hamiltonian on a three-dimensional lattice
JO  - Nanosistemy: fizika, himiâ, matematika
PY  - 2022
SP  - 237
EP  - 244
VL  - 13
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/NANO_2022_13_3_a0/
LA  - en
ID  - NANO_2022_13_3_a0
ER  - 
%0 Journal Article
%A M. I. Muminov
%A A. M. Khurramov
%A I. N. Bozorov
%T Conditions for the existence of bound states of a two-particle Hamiltonian on a three-dimensional lattice
%J Nanosistemy: fizika, himiâ, matematika
%D 2022
%P 237-244
%V 13
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/NANO_2022_13_3_a0/
%G en
%F NANO_2022_13_3_a0
M. I. Muminov; A. M. Khurramov; I. N. Bozorov. Conditions for the existence of bound states of a two-particle Hamiltonian on a three-dimensional lattice. Nanosistemy: fizika, himiâ, matematika, Tome 13 (2022) no. 3, pp. 237-244. http://geodesic.mathdoc.fr/item/NANO_2022_13_3_a0/