Supersymmetric one-parameter strict isospectrality for the attractive delta potentials

The Schr\"odinger equation with attractive delta potential has been previously studied in the supersymmetric quantum mechanical approach by a number of authors, but they all used only the particular superpotential solution. Here, we introduce a one-parameter family of strictly isospectral attractive delta function potentials, which is based on the general superpotential (general Riccati) solution, we study the problem in some detail and suggest possible applications