Article
Shifted One-Parameter Supersymmetric Family of Quartic Asymmetric Double-Well Potentials
Annals of Physics
(2014)
Abstract
Extending our previous work (Rosu, 2014), we define supersymmetric partner potentials through a particular Riccati solution of the form F(x)=(x−c)2−1, where c is a real shift parameter, and work out the quartic double-well family of one-parameter isospectral potentials obtained by using the corresponding general Riccati solution. For these parametric double well potentials, we study how the localization properties of the two wells depend on the parameter of the potentials for various values of the shifting parameter. We also consider the supersymmetric parametric family of the first double-well potential in the Razavy chain of double well potentials corresponding to F(x)=12sinh2x−2(1+2)sinh2x(1+2)cosh2x+1, both unshifted and shifted, to test and compare the localization properties.
Keywords
- Shifted quartic double well,
- Razavy potential,
- Zero mode,
- Localization,
- Riccati solution,
- Darboux deformation
Disciplines
Publication Date
October, 2014
DOI
https://doi.org/10.1016/j.aop.2014.06.008
Citation Information
S.C. Mancas, Haret C. Rosu and Pisin Chen. "Shifted One-Parameter Supersymmetric Family of Quartic Asymmetric Double-Well Potentials" Annals of Physics Vol. 349 (2014) p. 33 - 42 Available at: http://works.bepress.com/stefani_mancas/107/