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In the context of supersymmetric quantum mechanics, we define a potentialthrough a particular Riccati solution of the composition form, F(f(x)), andobtain a generalized Mielnik construction of one-parameter isospectralpotentials when we use the general Riccati solution. Some examples for specialcases of F and f are given to illustrate the method. An interesting result isobtained in the case of a parametric double well potential generated by thismethod, for which it is shown that the parameter of the potential controls theheights of the localization probability in the two wells, and for certainvalues of the parameter the height of the localization probability can behigher in the smaller well

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