The positive radial momentum operator
Mosley, Shaun N.
arXiv, 0309055 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2003-09-24
Classification:  Mathematical Physics,  81Q10 (Primary) 47G30 (Secondary) 
@article{0309055,
     author = {Mosley, Shaun N.},
     title = {The positive radial momentum operator},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0309055}
}

Mosley, Shaun N. The positive radial momentum operator. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0309055/