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This article is cited in 2 scientific papers (total in 2 papers)
MATHEMATICS
On eigenvalues and virtual levels of a two-particle Hamiltonian on a $d$-dimensional lattice
Mukhiddin I. Muminovab, Abdimajid M. Hurramova, Islom N. Bozorovab a Samarkand State University, Samarkand, Uzbekistan
b V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan
Abstract:
The two-particle Schrödinger operator $h_\mu(k)$, $k\in\mathbb{T}^d$ (where $\mu>0$, $\mathbb{T}^d$ is a $d$-dimensional torus), associated to the Hamiltonian h of the system of two quantum particles moving on a $d$-dimensional lattice, is considered as a perturbation of free Hamiltonian $h_0(k)$ by the certain $3^d$ rank potential operator $\mu\mathbf{v}$. The existence conditions of eigenvalues and virtual levels of $h_\mu(k)$, are investigated in detail with respect to the particle interaction $\mu$ and total quasi-momentum $k\in\mathbb{T}^d$.
Keywords:
two-particle Hamiltonian, invariant subspace, orthogonal projector, eigenvalue, virtual level, multiplicity of virtual level.
Received: 06.03.2023 Revised: 26.04.2023 Accepted: 27.04.2023
Citation:
Mukhiddin I. Muminov, Abdimajid M. Hurramov, Islom N. Bozorov, “On eigenvalues and virtual levels of a two-particle Hamiltonian on a $d$-dimensional lattice”, Nanosystems: Physics, Chemistry, Mathematics, 14:3 (2023), 295–303
Linking options:
https://www.mathnet.ru/eng/nano1192 https://www.mathnet.ru/eng/nano/v14/i3/p295
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