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 that cannot be measured simultaneously with the energy are chosen for the canonical quantizations. Another merit of the non-Hermitian representation is that it naturally allows us to introduce the generalized ladder operators with which one can solve eigenvalue problems quite neatly. © 1996 The American Physical Society.

• Received 24 July 1995

DOI:https://doi.org/10.1103/PhysRevA.53.1251