PT symmetry of a conditionally exactly solvable potential
  A conditionally exactly solvable potential, the supersymmetric partner of the harmonic oscillator is investigated in the PT-symmetric setting. It is shown that a number of properties characterizing shape-invariant and Natanzon-class potentials generated by an imaginary coordinate shift $x-{\rm i}\epsilon$ also hold for this potential outside the Natanzon class. 
Anjana Sinha, Geza Levai and Pinaki Roy