Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations

Details Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations

2008-05-02

arxiv.org/abs/0805.0166v3

SIGMA 5 (2009), 104, 16 pages

Physics

Mathematical Physics

Scientific paper

10.3842/SIGMA.2009.104

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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