Numerical approach to the ground and excited states of a Bose-Einstein condensed gas confined in a completely anisotropic trap

The ground and excited states of a weakly interacting and dilute Bose-Einst ein condensed gas, confined in a completely anisotropic harmonic oscillator potential, are determined at zero temperature within the Bogoliubov approx imation. The numerical calculations employ a computationally efficient proc edure based on a discrete variable representation (DVR) of the Hamiltonian. The DVR is efficient for problems where the interaction potential may be e xpressed as a local function of interparticle coordinates. In order to addr ess condensates that are both very large (similar to 10(6) atoms) and fully anisotropic, the ground state is found using a self-consistent held approa ch. Experience has demonstrated, however, that standard iterative technique s applied to the solution of the nonlinear partial differential equation fo r the condensate are nonconvergent. This limitation is overcome using the m ethod of direct inversion in the iterated subspace (DIIS). In addition, the sparse structure of the DVR enables die efficient application of iterative techniques such as the Davidson and/or Lanczos methods, to extract the eig envalues of physical interest. The results are compared with recent experim ental data obtained for Bose-Einstein condensed alkali-metal vapors confine d in magnetic traps. [S1050-2947(99)05803-5].