Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/15212
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dc.contributor.authorErman, Fatih-
dc.contributor.authorTurgut, O. Teoman-
dc.date.accessioned2024-12-25T20:49:33Z-
dc.date.available2024-12-25T20:49:33Z-
dc.date.issued2024-
dc.identifier.issn0002-9505-
dc.identifier.issn1943-2909-
dc.identifier.urihttps://doi.org/10.1119/5.0228452-
dc.identifier.urihttps://hdl.handle.net/11147/15212-
dc.description.abstractThere are a few exactly solvable potentials in quantum mechanics for which the completeness relation of the energy eigenstates can be explicitly verified. In this article, we give an elementary proof that the set of bound (discrete) states together with the scattering (continuum) states of the reflectionless potential form a complete set. We also review a direct and elegant derivation of the energy eigenstates with proper normalization by introducing an analog of the creation and annihilation operators of the harmonic oscillator problem. We further show that, in the case of a single bound state, the corresponding wave function can be found from the knowledge of continuum eigenstates of the system. Finally, completeness is shown by using the even/odd parity eigenstates of the Hamiltonian, which provides another explicit demonstration of a fundamental property of quantum mechanical Hamiltonians.en_US
dc.language.isoenen_US
dc.publisherAip Publishingen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subject[No Keyword Available]en_US
dc.titleCompleteness of Energy Eigenfunctions for the Reflectionless Potential in Quantum Mechanicsen_US
dc.typeArticleen_US
dc.departmentIzmir Institute of Technologyen_US
dc.identifier.volume92en_US
dc.identifier.issue12en_US
dc.identifier.startpage950en_US
dc.identifier.endpage956en_US
dc.identifier.wosWOS:001361758200013-
dc.identifier.scopus2-s2.0-85210747640-
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.identifier.doi10.1119/5.0228452-
dc.authorscopusid23102409500-
dc.authorscopusid56206920900-
dc.authorwosidErman, Fatih/J-6781-2019-
dc.identifier.wosqualityQ4-
dc.identifier.scopusqualityQ3-
dc.description.woscitationindexScience Citation Index Expanded-
item.languageiso639-1en-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.grantfulltextnone-
item.fulltextNo Fulltext-
item.openairetypeArticle-
item.cerifentitytypePublications-
crisitem.author.dept04.02. Department of Mathematics-
Appears in Collections:Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection
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