Classical-quantum correspondence for shape-invariant systems
arXiv:1405.0968 · doi:10.1088/1751-8113/48/24/245201
Abstract
A quantization procedure, which has recently been introduced for the analysis of Painlevé 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.