Abstract: A new decomposition of the momentum operator in curvilinear coordinates is proposed，from which

an equivalent operator of radial operator is resulted. Though the radial operator itself is non-self-adjoint and is not

measurable in physics，the equivalent operator is in fact the difference of two self-adjoint operators，so is measurable.

Thus，a superficial contradiction between the non-self-adjointness and existence of the uncertainty for the radial

momentum operator is resolved. What is more，the Hydrogen atom ground state is used to show how to measure

the equivalent operator.

Key words: radial momentum, geometric momentum, decomposition of momentum