# Ground state of the time-independent Gross–Pitaevskii equation

## Description

Abstract We present a suite of programs to determine the ground state of the time-independent Gross-Pitaevskii equation, used in the simulation of Bose-Einstein condensates. The calculation is based on the Optimal Damping Algorithm, ensuring a fast convergence to the true ground state. Versions are given for the one-, two-, and three-dimensional equation, using either a spectral method, well suited for harmonic trapping potentials, or a spatial grid. Title of program: GPODA Catalogue Id: ADZN_v1_0 Nature of problem The order parameter (or wave function) of a Bose-Einstein condensate (BEC) is obtained, in a mean field approximation, by the Gross-Pitaevskii equation (GPE)[1]. The GPE is a nonlinear Schrödinger-like equation, including here a confining potential. The stationary state of a BEC is obtained by finding the ground state of the time-independent GPE, ie, the order parameter that minimizes the energy. In addition to the standard three-dimensional GPE, tight traps can lead to effective two- or even on ... Versions of this program held in the CPC repository in Mendeley Data ADZN_v1_0; GPODA; 10.1016/j.cpc.2007.04.007 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)