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

Year 2016, Volume: 45 Issue: 6, 1693 - 1703, 01.12.2016

Saidakhmat Lakaev Ender Özdemir

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

References

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