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arXiv · 0911.3913

On the Thomas-Fermi ground state in a harmonic potential

Clément Gallo·Dmitry Pelinovsky
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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 Painlevé-II equation. In the space of one dimension, these results allow us to characterize the distribution of eigenvalues in the point spectrum of the Schrödinger operator associated with the nonlinear ground state.

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Clément Gallo, Dmitry Pelinovsky. 2009-11-19. On the Thomas-Fermi ground state in a harmonic potential. https://arxiv.org/abs/0911.3913

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