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

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Hacettepe Journal of Mathematics and Statistics
Volume:45 Issue:6
The existence and location of eigenvalues of the one particle Hamiltonians on lattices

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

Authors : Saidakhmat LAKAEV, Ender ÖZDEMİR

Pages : 1693-1703

View : 52 | Download : 8

Publication Date : 2016-12-01

Article Type : Research Paper

Abstract :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
Keywords : One particle Hamiltonian, essential spectrum, asymptotic, eigenvalue

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