  The non self-adjointness of the radial momentum operator has been noted
before by several authors, but the various proofs are incorrect. We give a
rigorous proof that the $n$-dimensional radial momentum operator is not self-
adjoint and has no self-adjoint extensions. The main idea of the proof is to
show that this operator is unitarily equivalent to the momentum operator on
$L^{2}[(0,\infty),dr]$ which is not self-adjoint and has no self-adjoint
extensions.
