Isospectral deformation of some shape invariant potentials

Here we generalize the isospectral deformation of the discrete eigenspectrum of Eleonsky and Korolev [Phys. Rev. A 55, 2580 (1997)] to continuous eigenspectrum of some well-known shape-invariant potentials. We show that the isospectral deformations preserve their shape invariance properties. Hence, using the preserved shape invariance property of the deformed potentials, we obtain both discrete and continuous eigenspectrum of the deformed Rosen–Morse, Natanzon, Rosen–Morse with added Dirac delta term, and Natanzon with added Dirac delta term potentials, respectively. It is shown that deformation does not change their other pecurialities, such as the reflectionless property of the Rosen–Morse potential and the penetrationless property of the Natanzon one.