How to generalize the Ehrenfest theorem and the uncertainty principle

The Ehrenfest theorem and the Robertson uncertainty relation are well-known basic equations in quantum mechanics. In both equations a commutator of two operators occurs, where for the Ehrenfest theorem one of these two operators is the Hamiltonian. For the correctness of the derivation of the Ehrenfest theorem, there arise problems if we use the azimuthal angle in polar or spherical coordinates as the other operator in this commutator. In addition, similar problems may occur for the derivation of the Robertson uncertainty relation if we use the azimuthal angle as one of the two operators in the commutator. As a consequence, there exist problematic cases, where the Ehrenfest theorem and the Robertson uncertainty relation are not correct. The purpose of this paper is to present and discuss a generalized Ehrenfest theorem and a generalized uncertainty relation being still valid for these problematic cases. Hereby, we define and use a mathematical operation called expectation commutator.