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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
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
📌 3 Key Takeaways
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Objective & Hypothesis:We consider a quantum particle moving in the one dimensional lattice Z and interacting with a indefinite sign external field vˆ.
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Key Findings & Data: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.
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Conclusion & Impact: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
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:One particle Hamiltonian · essential spectrum · asymptotic
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
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Cite This Article
ÖZDEMİR, E., LAKAEV, S. (2022). The existence and location of eigenvalues of the one particle Hamiltonians on lattices. Hacettepe Journal of Mathematics and Statistics, Cilt: 45 - Sayı: 6, 1693–1703. https://ajindex.com/articles/530029