Classical-quantum correspondence for shape-invariant systems

• Main Authors: Grundland, A. M, Riglioni, D
• Format: Journal Article
• Language: English
• Published: 24-08-2015
• Subjects: Mathematics - Mathematical Physics; Physics - Mathematical Physics
• DOI: 10.48550/arxiv.1405.0968

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.