Numerical Methods for the study of Bose-Einstein Condensates using the Gross-Pitaevskii Equation

The Gross-Pitaevskii equation (GPE) is a mean eld approximation used to study Bose-Einstein condensates (BEC). Here, we present a brief derivation of the GPE without the use of second quantization, as well as some of its consequences. Next, we present the implementation in Python of some numerical methods to compute the ground state of BEC. We compare the results with well known theoretical limits and the numerical results obtained using GPELab, a MATLAB toolbox to compute stationary and dynamic solutions of the GPE