  Quantum canonical transformations of the second kind and the non-Hermitian
realizations of the basic canonical commutation relations are investigated with
a special interest in the generalization of the conventional ladder operators.
The operator ordering problem is shown to be resolved when the non-Hermitian
realizations for the canonical variables which can not be measured
simultaneously with the energy are chosen for the canonical quantizations.
Another merit of the non-Hermitian representations is that it naturally allows
us to introduce the generalized ladder operators with which one can solve
eigenvalue problems quite neatly.
