2020/04/10 by Yuta Nasuda, Nasuda, Yuta, Nobuyuki Sawado +1
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2004.04927
openalex publication_date 2020/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ℏ-dependency from the condition, and it is satisfied with a certain degree of accuracy.