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Nonlinear Sciences > Exactly Solvable and Integrable Systems

arXiv:0712.2616 (nlin)
[Submitted on 17 Dec 2007]

Title:New Quasi Exactly Solvable Difference Equation

Authors:Ryu Sasaki
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Abstract: Exact solvability of two typical examples of the discrete quantum mechanics, i.e. the dynamics of the Meixner-Pollaczek and the continuous Hahn polynomials with full parameters, is newly demonstrated both at the Schroedinger and Heisenberg picture levels. A new quasi exactly solvable difference equation is constructed by crossing these two dynamics, that is, the quadratic potential function of the continuous Hahn polynomial is multiplied by the constant phase factor of the Meixner-Pollaczek type. Its ordinary quantum mechanical counterpart, if exists, does not seem to be known.
Comments: LaTeX with jnmp class, 12 pages, no figure, submitted for publication in the Proceedings of NEEDS 2007, which will be published as a special issue of Journal of Nonlinear mathematical Physics
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Classical Analysis and ODEs (math.CA)
Report number: YITP-o7-63
Cite as: arXiv:0712.2616 [nlin.SI]
  (or arXiv:0712.2616v1 [nlin.SI] for this version)
  https://doi.org/10.48550/arXiv.0712.2616
Related DOI: https://doi.org/10.2991/jnmp.2008.15.s3.36

Submission history

From: Ryu Sasaki [view email]
[v1] Mon, 17 Dec 2007 02:50:27 UTC (12 KB)
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