Bethe ansatz solutions to quasi exactly solvable difference equations

Sasaki, Ryu, Yang, Wen-Li and Zhang, Yao-Zhong (2009). Bethe ansatz solutions to quasi exactly solvable difference equations. In: Miloslav Znojil, Proceedings of the 5th Microconference Analytic and Algebraic Methods V. Analytic and Algebraic Methods V, Ukraine, Czech Republic, (104-1-104-16). May 27–28 2009. doi:10.3842/SIGMA.2009.104


Author Sasaki, Ryu
Yang, Wen-Li
Zhang, Yao-Zhong
Title of paper Bethe ansatz solutions to quasi exactly solvable difference equations
Conference name Analytic and Algebraic Methods V
Conference location Ukraine, Czech Republic
Conference dates May 27–28 2009
Proceedings title Proceedings of the 5th Microconference Analytic and Algebraic Methods V
Journal name Symmetry, Integrability and Geometry: Methods and Applications
Place of Publication Tereschenkivska, Ukraine
Publisher Natsional'na Akademiya Nauk Ukrainy
Publication Year 2009
Sub-type Article (original research)
DOI 10.3842/SIGMA.2009.104
Open Access Status DOI
ISSN 1815-0659
Editor Miloslav Znojil
Volume 5
Start page 104-1
End page 104-16
Total pages 16
Collection year 2010
Language eng
Abstract/Summary 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.
Keyword Bethe ansatz solution
Quasi-exactly solvable models
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Article # 104

 
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Created: Thu, 25 Feb 2010, 23:41:57 EST by Kay Mackie on behalf of School of Mathematics & Physics