On the Thomas-Fermi ground state in a harmonic potential
Mathematical Physics
2009-11-23 v1 math.MP
Abstract
We study nonlinear ground states of the Gross-Pitaevskii equation in the space of one, two and three dimensions with a radially symmetric harmonic potential. The Thomas-Fermi approximation of ground states on various spatial scales was recently justified using variational methods. We justify here the Thomas-Fermi approximation on an uniform spatial scale using the Painlev\'{e}-II equation. In the space of one dimension, these results allow us to characterize the distribution of eigenvalues in the point spectrum of the Schr\"{o}dinger operator associated with the nonlinear ground state.
Cite
@article{arxiv.0911.3913,
title = {On the Thomas-Fermi ground state in a harmonic potential},
author = {Clément Gallo and Dmitry Pelinovsky},
journal= {arXiv preprint arXiv:0911.3913},
year = {2009}
}
Comments
38 pages, no figures