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Title: One-parameter families of supersymmetric isospectral potentials from Riccati solutions in function composition form

In 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. -- Highlights: •Function-composition generalization of parametric isospectral potentials is presented. •Mielnik one-parameter family of harmonic potentials is obtained as a particular case. •Graphical discussion of regular and singular regions in the parameter space is given.
Authors:
 [1] ;  [2] ;  [3]
  1. IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Camino a la presa San José 2055, Col. Lomas 4a Sección, 78216 San Luis Potosí, S.L.P. (Mexico)
  2. Department of Mathematics, Embry–Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States)
  3. Leung Center for Cosmology and Particle Astrophysics (LeCosPA) and Department of Physics, National Taiwan University, Taipei 10617, Taiwan (China)
Publication Date:
OSTI Identifier:
22314789
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 343; Journal Issue: Complete; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CALCULATION METHODS; HARMONIC POTENTIAL; MATHEMATICAL SOLUTIONS; POTENTIALS; PROBABILITY; QUANTUM MECHANICS; RICCATI EQUATION; SUPERSYMMETRY