A New Class of PT-symmetric Hamiltonians with Real Spectra
  We investigate complex PT-symmetric potentials, associated with quasi-exactly solvable non-hermitian models involving polynomials and a class of rational functions. We also look for special solutions of intertwining relations of SUSY Quantum Mechanics providing a partnership between a real and a complex PT-symmetric potential of the kind mentioned above. We investigate conditions sufficient to ensure the reality of the full spectrum or, for the quasi-exactly solvable systems, the reality of the energy of the finite number of levels. 
F. Cannata (Bologna), M. Ioffe (St.Petersburg), R. Roychoudhury   (Calcutta) and P. Roy (Calcutta)