The supersymmetric WKB (SWKB) condition is supposed to be exact for all known exactly solvable quantum mechanical systems with the shape invariance. Recently, it was claimed that the SWKB condition was not exact for the extended radial oscillator, whose eigenfunctions consisted of the exceptional orthogonal polynomial, even the system possesses the shape invariance. In this paper, we examine the SWKB condition for the two novel classes of exactly solvable systems: one has the multi-indexed Laguerre and Jacobi polynomials as the main parts of the eigenfunctions, and the other has the Krein–Adler Hermite, Laguerre and Jacobi polynomials. For all of them, one can always remove the [Formula: see text]-dependency from the condition, and it is satisfied with a certain degree of accuracy.

中文翻译：

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新类精确可解系统的 SWKB 条件的数值研究

超对称 WKB (SWKB) 条件对于所有已知的具有形状不变性的完全可解的量子力学系统来说应该是精确的。最近，有人声称SWKB条件对于扩展径向振子并不精确，其特征函数由异常正交多项式组成，即使系统具有形状不变性。在本文中，我们研究了两类新的精确可解系统的 SWKB 条件：一类具有多索引 Laguerre 和 Jacobi 多项式作为特征函数的主要部分，另一类具有 Krein-Adler Hermite、Laguerre 和 Jacobi多项式。对于所有这些，总是可以从条件中去除[公式：见正文]-依赖性，并且满足一定程度的准确性。