Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations
Bethe ansatz formulation is presented for several explicit examples of quasi exactly solvable difference equations of one degree of freedom which are introduced recently by one of the present authors. These equations are deformation of the well-known exactly solvable difference equations of the Meix...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2009 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2009
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149104 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations / Ryu Sasaki, Wen-Li Yang, Yao-Zhong Zhang // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 24 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862549118508859392 |
|---|---|
| author | Sasaki, Ryu Yang, Wen-Li Zhang, Yao-Zhong |
| author_facet | Sasaki, Ryu Yang, Wen-Li Zhang, Yao-Zhong |
| citation_txt | Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations / Ryu Sasaki, Wen-Li Yang, Yao-Zhong Zhang // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 24 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Bethe ansatz formulation is presented for several explicit examples of quasi exactly solvable difference equations of one degree of freedom which are introduced recently by one of the present authors. These equations are deformation of the well-known exactly solvable difference equations of the Meixner-Pollaczek, continuous Hahn, continuous dual Hahn, Wilson and Askey-Wilson polynomials. Up to an overall factor of the so-called pseudo ground state wavefunction, the eigenfunctions within the exactly solvable subspace are given by polynomials whose roots are solutions of the associated Bethe ansatz equations. The corresponding eigenvalues are expressed in terms of these roots.
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| first_indexed | 2025-11-25T20:36:34Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149104 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T20:36:34Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Sasaki, Ryu Yang, Wen-Li Zhang, Yao-Zhong 2019-02-19T17:24:36Z 2019-02-19T17:24:36Z 2009 Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations / Ryu Sasaki, Wen-Li Yang, Yao-Zhong Zhang // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 24 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 35Q40; 37N20; 39A70; 82B23 https://nasplib.isofts.kiev.ua/handle/123456789/149104 Bethe ansatz formulation is presented for several explicit examples of quasi exactly solvable difference equations of one degree of freedom which are introduced recently by one of the present authors. These equations are deformation of the well-known exactly solvable difference equations of the Meixner-Pollaczek, continuous Hahn, continuous dual Hahn, Wilson and Askey-Wilson polynomials. Up to an overall factor of the so-called pseudo ground state wavefunction, the eigenfunctions within the exactly solvable subspace are given by polynomials whose roots are solutions of the associated Bethe ansatz equations. The corresponding eigenvalues are expressed in terms of these roots. This paper is a contribution to the Proceedings of the 5-th Microconference “Analytic and Algebraic Methods V”. The financial support from Australian Research Council is gratefully acknowledged. R.S. is supported in part by Grants-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology, No.18340061 and No.19540179. Y.Z.Z. thanks the Yukawa Institute for Theoretical Physics, Kyoto University for hospitality and financial support. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations Article published earlier |
| spellingShingle | Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations Sasaki, Ryu Yang, Wen-Li Zhang, Yao-Zhong |
| title | Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations |
| title_full | Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations |
| title_fullStr | Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations |
| title_full_unstemmed | Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations |
| title_short | Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations |
| title_sort | bethe ansatz solutions to quasi exactly solvable difference equations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149104 |
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