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