Angular-momentum—angle commutation relations and minimum-uncertainty states

We extend the canonical commutation relations (CCR) in quantum mechanics to the case where appropriate dynamical variables are angular momenta and angles. It is found that projection operators of the resultant Weyl algebra provide us with a new and powerful way of characterizing minimum-uncertainty states, including those obtained by Carruthers and Nieto. The uniqueness theorem of the Schroedinger representation remains valid for extended CCR in a simple case. Finally a wide range of applicability of our method is suggested.