形状不变系统的经典-量子对应
Classical-quantum correspondence for shape-invariant systems
摘要：
将最近引入的用于分析潘勒韦方程的量子化方法应用于牛顿方程的一般时间无关势。这一分析表明，量子化过程中保留的形状不变的潜力类的精确可解性。当一个一般的潜力被认为是量子化过程涉及的解决方案的甘比尔XXVII超越方程。明确的例子，涉及经典和例外的正交拉盖尔和雅可比多项式进行了讨论。
英文摘要：
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.
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