Numerical solution of the stationary Gross-Pitaevskii equation: tests of acombined 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 i nteracting condensate confined by a three-dimensional external potential wi th cylindrical symmetry. To this purpose we solve in imaginary time the non -linear Schrodinger 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 r esults against the textbook properties of stationary states. The latter are determined by using an explicit time-marching technique previously develop ed and successfully used to study the transport behaviour of such systems.