A new class of PT-symmetric Hamiltonians with real spectra

We investigate complex PT-symmetric potentials, associated with quasi-exact ly solvable non-Hermitian models involving polynomials and a class of ratio nal functions. We also look for special solutions of intertwining relations of SUSY quantum mechanics providing a partnership between a real and a com plex PT-symmetric potential of the kind mentioned above. We investigate con ditions sufficient to ensure the reality of the full spectrum or, for the q uasi-exactly solvable systems, the reality of the energy of the finite numb er of levels. (C) 2001 Elsevier Science B,V. All rights reserved.