Construction of self-similar shape invariant potentials with the Pade approximation
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AbstractWe study here the self-similar shape invariant potential (SSSIP) proposed by Barclay et al (1993 Phys. Rev. A 48 2786) in the context of supersymmetric quantum mechanics. The superpotential of SSSIP, W(x), obeys an ordinary differential equation involving W and its derivative at two different spatial points, and hence cannot be solved with standard numerical methods. In addition, Taylor series expansion of W(x) about x = 0 also diverges at large x. To provide an effective numerical scheme to construct the superpotential, we use the Pade approximation to express W(x) as a fraction of polynomials in x. We find that the homogeneous two-point Pade approximant can indeed yield accurate values of the superpotential for all x.
All Author(s) ListLau HK, Leung PT
Journal nameJournal of Physics A: Mathematical and Theoretical
Volume Number41
Issue Number2
LanguagesEnglish-United Kingdom
Web of Science Subject CategoriesPhysics; Physics, Mathematical; PHYSICS, MATHEMATICAL; Physics, Multidisciplinary; PHYSICS, MULTIDISCIPLINARY

Last updated on 2020-15-09 at 03:08