  The Gross-Pitaevskii equation (GP), that describes the wave function of a
number of coherent Bose particles contained in a trap, contains the cube of the
normalized wave function, times a factor proportional to the number of coherent
atoms. The square of the wave function, times the above mentioned factor, is
defined as the Hartree potential. A method implemented here for the numerical
solution of the GP equation consists in obtaining the Hartree potential
iteratively, starting with the Thomas Fermi approximation to this potential.
The energy eigenvalues and the corresponding wave functions for each successive
potential are obtained by a method described previously. After approximately 35
iterations a stability of eight significant figures for the energy eigenvalues
is obtained.This method has the advantage of being physically intuitive, and
could be extended to the calculation of a shell-model potential in nuclear
physics, once the Pauli exclusion principle is allowed for.
