Exactly solvable models with PT-symmetry and with an asymmetric coupling of channels

Abstract

Bound states generated by K coupled PT-symmetric square wells are studied in a series of models where the Hamiltonians are assumed $R-$pseudo-Hermitian and $R^2-$symmetric. Specific rotation-like generalized parities $R$ are considered such that $R^N=I$ at some integers N. We show that and how our assumptions make the models exactly solvable and quasi-Hermitian. This means that they possess the real spectra as well as the standard probabilistic interpretation.

22 p., submitted and to be presented, this week, to PHHQP IV Int. Workshop in Stellenbosch (http://academic.sun.ac.za/workshop)

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• The Pauli equation with complex boundary conditions
• Dynamics of charged fluids and 1/L perturbation expansions
• Double complex SUSY-transformations: deformations of real potentials and their spectral characteristics