The Existence and location of eigenvalues of the one particle Hamiltonians on lattices | Zendy

Saidalhmat Lakaev | Zendy

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The Existence and location of eigenvalues of the one particle Hamiltonians on lattices

Author(s) -

Saidalhmat Lakaev

Publication year - 2016

Publication title -

hacettepe journal of mathematics and statistics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.312

H-Index - 26

ISSN - 1303-5010

DOI - 10.15672/hjms.20164515685

Subject(s) - mathematics , eigenvalues and eigenvectors , pure mathematics , particle (ecology) , quantum mechanics , physics , oceanography , geology

We consider a quantum particle moving in the one dimensional lattice Z and interacting with a indefinite sign external field vˆ. We prove that the associated Hamiltonian H can have one or two eigenvalues, situated as below the bottom of the essential spectrum, as well as above the its top. Moreover, we show that the operator H can have two eigenvalues outside of the essential spectrum and one of them is situated below the bottom of the essential spectrum, and other one above its top

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