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Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2009, том 5
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Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations
Інший ID:
2000 Mathematics Subject Classification: 35Q40; 37N20; 39A70; 82B23
Посилання:
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.
Підтримка:
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.
Дата:
2009
Переглядів:
526
Завантажень:
238
Анотація:
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.
