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Spectral Features of Two-Particle Schrödinger Operator on d-Dimensiional Lattice

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Abstract

This paper reports the spectral features of two-particle Schrödinger Hamiltonian operator on d-dimensional lattice \({{\mathbb {Z}}}^d\). A family of operators h(k) was emanated after the “separation of the center of mass” of a system of two particles depending on the values of total quasimomentum \(k\in {{\mathbb {T}}}^d\), (where \({{\mathbb {T}}}^d\) is d-dimensional torus). A sufficiency condition was achieved for the finiteness of the number of embedded and discrete eigenvalues of h(k) for any fixed \(k\in {{\mathbb {T}}}^d.\)

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Correspondence to Mukhiddin I. Muminov.

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Communicated by Sergey Naboko.

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This article is part of the topical collection “Spectral Theory and Operators in Mathematical Physics” edited by Jussi Behrndt, Fabrizio Colombo and Sergey Naboko.

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Muminov, M.I., Ghoshal, S.K. Spectral Features of Two-Particle Schrödinger Operator on d-Dimensiional Lattice. Complex Anal. Oper. Theory 14, 11 (2020). https://doi.org/10.1007/s11785-019-00978-z

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