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arXiv · 1405.0968

Classical-quantum correspondence for shape-invariant systems

A. M. Grundland·D. Riglioni
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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.

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A. M. Grundland, D. Riglioni. 2014-05-05. Classical-quantum correspondence for shape-invariant systems. https://doi.org/10.1088/1751-8113/48/24/245201

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