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This article is cited in 16 scientific papers (total in 16 papers)
Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations
Ryu Sasakia, Wen-Li Yangbc, Yao-Zhong Zhangc a Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
b Institute of Modern Physics, Northwest University, Xian 710069, P. R. China
c School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072, Australia
Abstract:
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.
Keywords:
Bethe ansatz solution; quasi-exactly solvable models.
Received: September 20, 2009; in final form November 10, 2009; Published online November 18, 2009
Citation:
Ryu Sasaki, Wen-Li Yang, Yao-Zhong Zhang, “Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations”, SIGMA, 5 (2009), 104, 16 pp.
Linking options:
https://www.mathnet.ru/eng/sigma450 https://www.mathnet.ru/eng/sigma/v5/p104
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