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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.
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