New Quasi Exactly Solvable Difference Equation

Nonlinear Sciences – Exactly Solvable and Integrable Systems

Scientific paper

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LaTeX with jnmp class, 12 pages, no figure, submitted for publication in the Proceedings of NEEDS 2007, which will be publishe

Scientific paper

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.

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