Quantum operators in generalized coordinates

Abstract

It will be shown in this paper how to build quantum operators in generalized coordinates. A direct substitution of momentum operators in the classical expression suffices; the only condition being that this expression must be written in matrix form before the substitution. Specifically, we are then able to show that the two operators −ih/(∂/∂Q) and −ih/g−1/2 (∂/∂Q)g1/2, and only these, are to be associated with generalized momenta.