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Article
One-Parameter Families of Isospectral Potentials from Riccati Solutions in Function Composition Form
Annals of Physics (2014)
  • Haret C. Rosu, Instituto Potosino de Investigacion Cientifica y Tecnologica
  • Stefan C. Mancas, Embry-Riddle Aeronautical University
  • Pisin Chen, National Taiwan University
Abstract
n the context of supersymmetric quantum mechanics, we define a potential through a particular Riccati solution of the composition form (F∘f)(x)=F(f(x)) and obtain a generalized Mielnik construction of one-parameter isospectral potentials when we use the general Riccati solution. Some examples for special cases of F and f are given to illustrate the method. An interesting result is obtained in the case of a parametric double well potential generated by this method, for which it is shown that the parameter of the potential controls the heights of the localization probability in the two wells, and for certain values of the parameter the height of the localization probability can be higher in the smaller well.
Keywords
  • isospectral potentials,
  • function composition,
  • integrating factor,
  • zero mode,
  • Riccati equation
Publication Date
April, 2014
DOI
https://doi.org/10.1016/j.aop.2014.01.012
Citation Information
Haret C. Rosu, Stefan C. Mancas and Pisin Chen. "One-Parameter Families of Isospectral Potentials from Riccati Solutions in Function Composition Form" Annals of Physics Vol. 343 (2014) p. 87 - 102 ISSN: 0003-4916
Available at: http://works.bepress.com/stefan_mancas/4/