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

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