Spectral Analysis of Certain Schrödinger Operators
The J-matrix method is extended to difference and q-difference operators and is applied to several explicit differential, difference, q-difference and second order Askey-Wilson type operators. The spectrum and the spectral measures are discussed in each case and the corresponding eigenfunction expan...
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| Дата: | 2012 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2012
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148463 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Spectral Analysis of Certain Schrödinger Operators / Mourad E.H. Ismail, E. Koelink // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 40 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1484632019-02-19T01:24:47Z Spectral Analysis of Certain Schrödinger Operators Ismail, Mourad E.H. Koelink, E The J-matrix method is extended to difference and q-difference operators and is applied to several explicit differential, difference, q-difference and second order Askey-Wilson type operators. The spectrum and the spectral measures are discussed in each case and the corresponding eigenfunction expansion is written down explicitly in most cases. In some cases we encounter new orthogonal polynomials with explicit three term recurrence relations where nothing is known about their explicit representations or orthogonality measures. Each model we analyze is a discrete quantum mechanical model in the sense of Odake and Sasaki [J. Phys. A: Math. Theor. 44 (2011), 353001, 47 pages]. 2012 Article Spectral Analysis of Certain Schrödinger Operators / Mourad E.H. Ismail, E. Koelink // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 40 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 30E05; 33C45; 39A10; 42C05; 44A60 DOI: http://dx.doi.org/10.3842/SIGMA.2012.061 http://dspace.nbuv.gov.ua/handle/123456789/148463 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The J-matrix method is extended to difference and q-difference operators and is applied to several explicit differential, difference, q-difference and second order Askey-Wilson type operators. The spectrum and the spectral measures are discussed in each case and the corresponding eigenfunction expansion is written down explicitly in most cases. In some cases we encounter new orthogonal polynomials with explicit three term recurrence relations where nothing is known about their explicit representations or orthogonality measures. Each model we analyze is a discrete quantum mechanical model in the sense of Odake and Sasaki [J. Phys. A: Math. Theor. 44 (2011), 353001, 47 pages]. |
| format |
Article |
| author |
Ismail, Mourad E.H. Koelink, E |
| spellingShingle |
Ismail, Mourad E.H. Koelink, E Spectral Analysis of Certain Schrödinger Operators Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Ismail, Mourad E.H. Koelink, E |
| author_sort |
Ismail, Mourad E.H. |
| title |
Spectral Analysis of Certain Schrödinger Operators |
| title_short |
Spectral Analysis of Certain Schrödinger Operators |
| title_full |
Spectral Analysis of Certain Schrödinger Operators |
| title_fullStr |
Spectral Analysis of Certain Schrödinger Operators |
| title_full_unstemmed |
Spectral Analysis of Certain Schrödinger Operators |
| title_sort |
spectral analysis of certain schrödinger operators |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148463 |
| citation_txt |
Spectral Analysis of Certain Schrödinger Operators / Mourad E.H. Ismail, E. Koelink // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 40 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT ismailmouradeh spectralanalysisofcertainschrodingeroperators AT koelinke spectralanalysisofcertainschrodingeroperators |
| first_indexed |
2023-05-20T17:30:44Z |
| last_indexed |
2023-05-20T17:30:44Z |
| _version_ |
1796153465777422336 |