The positive radial momentum operator

Abstract

The Laplacian in spherical coordinates contains the squared radial momentum operator $p_r^2=-r^{-1}{\partial }_r^{2}r$ which is Hermitian and positive. However as has been pointed out by various authors the ``radial momentum operator" $-i{r}^{-1}{\partial }_{r}r$ is not Hermitian. The positive square root operator of $p_r^2$ is found and also its inverse. We discuss the relation of these operators with Fourier transforms, the Hilbert transform and fractional integral operators.

5 pages, plainTex