Geodesic
On eigenvalues and virtual levels of a two-particle Hamiltonian on a $d$-dimensional lattice
Nanosistemy: fizika, himiâ, matematika, Tome 14 (2023) no. 3, pp. 295-303

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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. 
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     author = {Mukhiddin I. Muminov and Abdimajid M. Hurramov and Islom N. Bozorov},
     title = {On eigenvalues and virtual levels of a two-particle {Hamiltonian} on a $d$-dimensional lattice},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {295--303},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2023_14_3_a0/}
}
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Mukhiddin I. Muminov; Abdimajid M. Hurramov; Islom N. Bozorov. On eigenvalues and virtual levels of a two-particle Hamiltonian on a $d$-dimensional lattice. Nanosistemy: fizika, himiâ, matematika, Tome 14 (2023) no. 3, pp. 295-303. http://geodesic.mathdoc.fr/item/NANO_2023_14_3_a0/