From Non-Hermitian Oscillator-like Operators to Freud Polynomials and Some Consequences

Abstract

We discuss families of non-Hermitian Hamiltonians dealing with oscillator-like interactions realized in terms of Heisenberg operators which are no more adjoint to each other. Specific differential realizations lead to real spectra and to eigenfunctions including Freud orthogonal polynomials. Some implications are also presented in connection with corresponding non-Hermitian position and momentum operators.