0 PT − symetric regularization and the new shape - invariant potentials

All the well known exactly solvable s−wave potentials V (r), r ∈ (0, ∞) may be PT −symmetrically regularized (say, by a " small " imaginary shift of the coordinate axis) and redefined as acting on the whole real line, r → x−i ε, x ∈ (−∞, ∞). There is no surprise that the new models are still exactly solvable and that their energies remain real. What is an unexpected result? The observed drastic and unpredictable changes in the forms of the new spectra themselves.