Comparison between the numerical solutions and the Thomas-Fermi   approximation for atomic-molecular Bose-Einstein condensates
  We study the stationary solution of an atomic Bose-Einstein condensate coupled coherently to a molecular condensate with both repulsive and attractive interspecies interactions confined in an isotropic harmonic trap. We use the Thomas-Fermi approximation and find four kinds of analytical solution for the cases. These analytical solutions are adopted as trial function for the diffusive numerical solution of the Gross-Pitaevskii equations. For the repulsive interspecies interaction, the case in which the atomic and molecular wavefunctions are out-phase, the densities have similar profiles for both methods, however, the case where the wavefunctions are in-phase, there are considerable difference between the density profiles. For the attractive interspecies interaction, there are two cases in the Thomas Fermi approximation where the wavefunctions are in-phase. One of them has numerical solution that agree with the approximation and the other does not have corresponding numerical solution. 
Leonardo S. F. Santos, Marcelo O. C. Pires, Davi Giugno
cond-mat.quant-gas