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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| Date: | 2009 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2009
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149104 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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nasplib_isofts_kiev_ua-123456789-1491042025-02-09T10:27:43Z Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations Sasaki, Ryu Yang, Wen-Li Zhang, Yao-Zhong 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. 2009 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications application/pdf Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Sasaki, Ryu Yang, Wen-Li Zhang, Yao-Zhong |
| spellingShingle |
Sasaki, Ryu Yang, Wen-Li Zhang, Yao-Zhong Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Sasaki, Ryu Yang, Wen-Li Zhang, Yao-Zhong |
| author_sort |
Sasaki, Ryu |
| title |
Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations |
| title_short |
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_sort |
bethe ansatz solutions to quasi exactly solvable difference equations |
| publisher |
Інститут математики НАН України |
| publishDate |
2009 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149104 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2025-11-25T20:36:34Z |
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2025-11-25T20:36:34Z |
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