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dc.contributor.authorAktosun, Tuncay ( )
dc.contributor.authorChoque-Rivero, Abdon E. ( Orcid Icon 0000-0003-0226-9612 )
dc.contributor.authorPapanicolaou, Vassilis ( Orcid Icon 0000-0001-5405-7297 )
dc.date.accessioned2021-10-18T18:23:17Z
dc.date.available2021-10-18T18:23:17Z
dc.date.issued2019-02-11
dc.identifier.citationAktosun, T., Choque-Rivero, A. E., & Papanicolaou, V. G. (2019). Bound states of the discrete Schrödinger equation with compactly supported potentials. Electronic Journal of Differential Equations, 2019(23), pp. 1-19.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/14669
dc.description.abstractThe discrete Schrödinger operator is considered on the half-line lattice n ∈ {1, 2, 3,...} with the Dirichlet boundary condition at n =0. It is assumed that the potential belongs to class Ab, i.e. it is real valued, vanishes when n > b with b being a fixed positive integer, and is nonzero at n = b. The proof is provided to show that the corresponding number of bound states, N, must satisfy the inequalities 0 ≤ N ≤ b. It is shown that for each fixed nonnegative integer k in the set {0, 1, 2,..., b}, there exist infinitely many potentials in class Ab for which the corresponding Schrödinger operator has exactly k bound states. Some auxiliary results are presented to relate the number of bound states to the number of real resonances associated with the corresponding Schrödinger operator. The theory presented is illustrated with some explicit examples.en_US
dc.formatText
dc.format.extent19 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2019, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectDiscrete Schrödinger operatoren_US
dc.subjectHalf-line latticeen_US
dc.subjectBound statesen_US
dc.subjectResonancesen_US
dc.subjectCompactly-supported potentialen_US
dc.subjectNumber of bound statesen_US
dc.titleBound states of the discrete Schrödinger equation with compactly supported potentialsen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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