Year: 2003
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Mosley, Shaun N.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2145135586