On the number of bound states for the one-dimensional Schrödinger equation
| dc.contributor | Virginia Tech | en |
| dc.contributor.author | Aktosun, T. | en |
| dc.contributor.author | Klaus, Martin | en |
| dc.contributor.author | van der Mee, Cornelis | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessed | 2014-03-20 | en |
| dc.date.accessioned | 2014-04-09T18:12:24Z | en |
| dc.date.available | 2014-04-09T18:12:24Z | en |
| dc.date.issued | 1998-09 | en |
| dc.description.abstract | The 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.sponsorship | NSF DMS-9501053 | en |
| dc.description.sponsorship | CNR | en |
| dc.description.sponsorship | MURST | en |
| dc.description.sponsorship | University of Cagliari Coordinated Research Grant | en |
| dc.identifier.citation | Aktosun, 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/10.1063/1.532510 | en |
| dc.identifier.doi | https://doi.org/10.1063/1.532510 | en |
| dc.identifier.issn | 0022-2488 | en |
| dc.identifier.uri | http://hdl.handle.net/10919/47072 | en |
| dc.identifier.url | http://scitation.aip.org/content/aip/journal/jmp/39/9/10.1063/1.532510 | en |
| dc.language.iso | en_US | en |
| dc.publisher | AIP Publishing | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject | inverse scattering | en |
| dc.subject | factorization | en |
| dc.subject | potentials | en |
| dc.subject | matrix | en |
| dc.subject | line | en |
| dc.title | On the number of bound states for the one-dimensional Schrödinger equation | en |
| dc.title.serial | Journal of Mathematical Physics | en |
| dc.type | Article - Refereed | en |
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