Classical-quantum correspondence for shape-invariant systems
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.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- June 2015
- DOI:
- 10.1088/1751-8113/48/24/245201
- arXiv:
- arXiv:1405.0968
- Bibcode:
- 2015JPhA...48x5201G
- Keywords:
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- Mathematical Physics;
- 35Q40;
- 33C45;
- 33C47
- E-Print:
- doi:10.1088/1751-8113/48/24/245201