On the number of bound states for the one-dimensional Schrödinger equation

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dc.contributorVirginia Techen
dc.contributor.authorAktosun, T.en
dc.contributor.authorKlaus, Martinen
dc.contributor.authorvan der Mee, Cornelisen
dc.contributor.departmentMathematicsen
dc.date.accessed2014-03-20en
dc.date.accessioned2014-04-09T18:12:24Zen
dc.date.available2014-04-09T18:12:24Zen
dc.date.issued1998-09en
dc.description.abstractThe number of bound states of the one-dimensional Schrodinger equation is analyzed in terms of the number of bound states corresponding to ''fragments'' of the potential. When the potential is integrable and has a finite first moment, the sharp inequalities 1 -p + Sigma(j=1)(p) N(j)less than or equal to N less than or equal to Sigma(j=1)(p) N-j are proved, where p is the number of fragments, N is the total number of bound states, and N-j is the number of bound states for the jth fragment. When p=2 the question of whether N=N-1 +N-2 or N=N-1+N-2-1 is investigated in detail. An illustrative example is also provided. (C) 1998 American Institute of Physics.en
dc.description.sponsorshipNSF DMS-9501053en
dc.description.sponsorshipCNRen
dc.description.sponsorshipMURSTen
dc.description.sponsorshipUniversity of Cagliari Coordinated Research Granten
dc.format.mimetypeapplication/pdfen
dc.identifier.citationAktosun, T.; Klaus, M.; van der Mee, C., "On the number of bound states for the one-dimensional Schrödinger equation," J. Math. Phys. 39, 4249 (1998); http://dx.doi.org/10.1063/1.532510en
dc.identifier.doihttps://doi.org/10.1063/1.532510en
dc.identifier.issn0022-2488en
dc.identifier.urihttp://hdl.handle.net/10919/47072en
dc.identifier.urlhttp://scitation.aip.org/content/aip/journal/jmp/39/9/10.1063/1.532510en
dc.language.isoenen
dc.publisherAIP Publishingen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectinverse scatteringen
dc.subjectfactorizationen
dc.subjectpotentialsen
dc.subjectmatrixen
dc.subjectlineen
dc.titleOn the number of bound states for the one-dimensional Schrödinger equationen
dc.title.serialJournal of Mathematical Physicsen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten

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