The existence and location of eigenvalues of the one particle discrete Schroedinger operators

Saidakhmat N. Lakaev; Ender Ozdemir

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arXiv · 1505.03645

The existence and location of eigenvalues of the one particle discrete Schroedinger operators

Saidakhmat N. Lakaev·Ender Ozdemir

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Abstract

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

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BibTeX RIS

Saidakhmat N. Lakaev, Ender Ozdemir. 2015-05-14. The existence and location of eigenvalues of the one particle discrete Schroedinger operators. https://arxiv.org/abs/1505.03645

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