Conditions for the existence of bound states of a two-particle Hamiltonian on a three-dimensional lattice
https://doi.org/10.17586/2220-8054-2022-13-3-237-244
Abstract
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 hμ(k), k∈T3, μ∈R associated to the Hamiltonian h, are studied depending on the energy of the particle interaction μ∈R and total quasi-momentum k∈T3 (T3 - three-dimensional torus).
About the Authors
M. I. Muminov
Samarkand State University; V. I. Romanovskiy Institute of Mathematics
Russian Federation
Russian Federation
A. M. Khurramov
Samarkand State University
Russian Federation
Russian Federation
I. N. Bozorov
Samarkand State University
Russian Federation
Russian Federation
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Review
For citations:
Muminov M.I., Khurramov A.M., Bozorov I.N. Conditions for the existence of bound states of a two-particle Hamiltonian on a three-dimensional lattice. Nanosystems: Physics, Chemistry, Mathematics. 2022;13(3):237-244. https://doi.org/10.17586/2220-8054-2022-13-3-237-244
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