Classical-quantum correspondence for shape-invariant systems
Mathematical Physics
2015-09-02 v2 math.MP
Abstract
A quantization procedure, which has recently been introduced for the analysis of Painlev\'e equations, is applied to a general time-independent potential of a Newton equation. This analysis shows that the quantization procedure preserves the exact solvability property for the class of shape-invariant potentials. When a general potential is considered the quantization procedure involves the solution of a Gambier XXVII transcendental equation. Explicit examples involving classical and exceptional orthogonal Laguerre and Jacobi polynomials are discussed.
Keywords
Cite
@article{arxiv.1405.0968,
title = {Classical-quantum correspondence for shape-invariant systems},
author = {A. M. Grundland and D. Riglioni},
journal= {arXiv preprint arXiv:1405.0968},
year = {2015}
}