On the Thomas–Fermi ground state in a harmonic potential | Zendy

Clément Gallo | Zendy; Dmitry E. Pelinovsky | Zendy

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On the Thomas–Fermi ground state in a harmonic potential

Author(s) -

Clément Gallo,

Dmitry E. Pelinovsky

Publication year - 2011

Publication title -

asymptotic analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.576

H-Index - 45

eISSN - 1875-8576

pISSN - 0921-7134

DOI - 10.3233/asy-2011-1034

Subject(s) - ground state , fermi gamma ray space telescope , physics , harmonic , state (computer science) , harmonic potential , quantum electrodynamics , quantum mechanics , mathematics , algorithm

We study nonlinear ground states of the Gross-Pitaevskii equation in thespace of one, two and three dimensions with a radially symmetric harmonicpotential. The Thomas-Fermi approximation of ground states on various spatialscales was recently justified using variational methods. We justify here theThomas-Fermi approximation on an uniform spatial scale using thePainlev\'{e}-II equation. In the space of one dimension, these results allow usto characterize the distribution of eigenvalues in the point spectrum of theSchr\"{o}dinger operator associated with the nonlinear ground state.

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