New Quasi-Exactly Solvable Difference Equation

DOI

10.2991/jnmp.2008.15.s3.36How to use a DOI?

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 Schr¨odinger and Heisenberg picture levels. A new quasiexactly solvable difference equation is constructed by crossing these two dynamics, that is, the quadratic potential function of the continuous Hahn polynomials 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.

Copyright

© 2008, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Ryu Sasaki
PY  - 2008
DA  - 2008/10/01
TI  - New Quasi-Exactly Solvable Difference Equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 373
EP  - 384
VL  - 15
IS  - supplement 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2008.15.s3.36
DO  - 10.2991/jnmp.2008.15.s3.36
ID  - Sasaki2008
ER  -