Numerical solution to the time-independent Gross-Pitaevskii equation

TL;DR

This paper presents a pseudospectral numerical method to solve the time-independent Gross-Pitaevskii equation for Bose-Einstein condensates in anisotropic traps, validating results against existing literature.

Contribution

It introduces a pseudospectral approach for solving the equation and compares numerical results with previous studies, demonstrating accuracy for moderate interaction strengths.

Findings

Numerical energies and chemical potentials agree with literature for weak to moderate interactions.

The method is effective for positive and negative scattering lengths.

Results are consistent with known physical behavior of Bose-Einstein condensates.

Abstract

We solve the time-independent Gross-Pitaevskii equation modeling the Bose-Einstein condensate trapped in an anistropic harmonic potential using a pseudospectral method. Numerically obtained values for an energy and a chemical potential for the condensate with positive and negative scattering length have been compared with those from the literature. The results show that they are in good agreement when an atomic interaction is not too strong.