论文标题
新型可解决系统的新型类别的SWKB条件的数值研究
Numerical study of the SWKB condition of novel classes of exactly solvable systems
论文作者
论文摘要
对于具有形状不变性的所有已知可解决的量子机械系统，Supersymmortric WKB（SWKB）条件应该是准确的。最近，有人声称SWKB条件对于扩展的径向振荡器并不确切，其本征函数由特殊的正交多项式组成，甚至系统都具有ShapeInvariance。本征函数，另一个具有Krein-Adler Hermite，Laguerre和Jacobipolynomial。对于所有人，一个人总是可以从这种情况中删除$ \ hbar $依赖性，并且对一定程度的准确性感到满意。
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 the exceptional orthogonal polynomial, even the system possesses the shapeinvariance.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 Jacobipolynomials.For all of them, one can always remove the $\hbar$-dependency from the condition, and it is satisfied with a certain degree of accuracy.
