Статья

On the existence of eigenvalues of the one particle discrete Schrödinger operators

A. M. KhalkhuzhaevInstitute of Mathematics named after V.I. Romanovsky at the Academy of Sciences of the Republic of Uzbekistan, 15, University boulevard, 140104 Samarkand, UzbekistanSh. I. KhamidovInstitute of Mathematics named after V.I. Romanovsky at the Academy of Sciences of the Republic of Uzbekistan, 15, University boulevard, 140104 Samarkand, UzbekistanHabibullo MahmudovSamarkand State University, 15, University boulevard, 140104 Samarkand, Uzbekistan

AIP conference proceedingsjournal2024en

ABI

Аннотация

We study the spectral properties of the Schrödinger-type operator H^=H^0+V^⁠, describing the motion of one quantum particle in the one-dimensional lattice ℤ in an indefinite sign external field v^⁠. We obtain sufficient conditions for the existence of eigenvalues of the operator H^ lying on either below the bottom of the essential spectrum or above its top.

Темы

Spectral Theory in Mathematical Physics Quantum chaos and dynamical systems Numerical methods in inverse problems

Идентификаторы

DOI: 10.1063/5.0200550

Цитирования и источники

Цитирований: 5 Использованных источников: 21

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