A self-adjoint decomposition of radial momentum implies that Dirac's introduction of the operator is insightful

With acceptance of the Dirac’s observation that the \textit{canonical quantization entails using Cartesian coordinates, }we examine the$$% operator ${\mathbf{e}}_r{P}_r$ rather than $P_r$ itself and demonstrate that there is a decomposition of ${\mathbf{e}}_r{P}_r$ into two self-adjoint but non-commutative parts, in which one is the total momentum and another is the transverse one. This study renders the operator $P_r$ indirectly measurable and physically meaningful.