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A new class of PT-symmetric Hamiltonians with real spectra. (English) Zbl 0984.81041

Summary: 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.

MSC:

81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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