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Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations
Symmetry, integrability and geometry: methods and applications, Tome 5 (2009) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {Bethe {Ansatz} {Solutions} to {Quasi} {Exactly} {Solvable} {Difference} {Equations}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a103/}
}
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Ryu Sasaki; Wen-Li Yang; Yao-Zhong Zhang. Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations. Symmetry, integrability and geometry: methods and applications, Tome 5 (2009). http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a103/

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