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Numerical solution of the two-dimensional Gross–Pitaevskii equation for trapped interacting atoms

✍ Scribed by Sadhan K. Adhikari

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
122 KB
Volume
265
Category
Article
ISSN
0375-9601

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✦ Synopsis

We present a numerical scheme for solving the time-independent nonlinear Gross-Pitaevskii equation in two dimensions describing the Bose-Einstein condensate of trapped interacting neutral atoms at zero temperature. The trap potential is taken to be of the harmonic-oscillator type and the interaction both attractive and repulsive. The Gross-Pitaevskii equation is numerically integrated consistent with the correct boundary conditions at the origin and in the asymptotic region. Rapid convergence is obtained in all cases studied. In the attractive case there is a limit to the maximum number of atoms in the condensate.

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Motivated by current experimental and theoretical activity in the field of BoseEinstein condensation of trapped vapours of alkali atoms, we implement the calculation of the ground-state energy and wave function of a dilute interacting condensate confined by a three-dimensional external potential wit