= Radial momentum operator
{title2=$p_r=-i\hbar(\partial_r+1/r)$}
For three-dimensional radial <wavefunctions> with measure $r^2dr$, this formal symmetric <momentum> expression obeys $[f(r),p_r]=i\hbar f'(r)$ on appropriate test functions and has square $-\hbar^2(\partial_r^2+2\partial_r/r)$. It is useful in separating <kinetic energy> as $p^2=p_r^2+L^2/r^2$. Formal <symmetry> and these identities do not establish a self-adjoint <momentum> observable on the half-line; domains and origin conditions must be specified when taking adjoints or defining products.
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