Shifted one-parameter supersymmetric family of quartic asymmetric double-well potentials

• Quartic one-parameter DWs with an additional shift parameter are introduced.
• Anomalous localization feature of their zero modes is confirmed at different shifts.
• Razavy one-parameter DWs are also introduced and shown not to have this feature.

Extending our previous work (Rosu, 2014), we define supersymmetric partner potentials through a particular Riccati solution of the form F(x)=(x−c)2−1F(x)=(x−c)2−1, where cc 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.