Numerical solution of the stationary Gross-Pitaevskii equation: tests of a combined imaginary-time-marching technique with splitting

Motivated by current experimental and theoretical activity in the field of Bose-Einstein 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 with cylindrical symmetry. To this purpose we solve in imaginary time the non-linear Schrödinger equation governing the dynamics of the condensate wave function by a splitting of the nonlinear term. The good and the bad of the method are analyzed by testing the simulation results against the textbook properties of stationary states. The latter are determined by using an explicit time-marching technique previously developed and successfully used to study the transport behaviour of such systems.