Quantum oscillations in a two-mode atom-molecule Bose-Einstein   condensate -- the discrete WKB approach
  Quantum effects in a system of coupled atomic and molecular Bose-Einstein condensates in the framework of a two-mode model are studied numerically and analytically, using the discrete WKB approach. In contrast to the mean-field approximation, the WKB analytical results are in a very good agreement with numerical results. The quantum fluctuations of the atomic and molecular populations are calculated, and found to be of the same order of magnitude as their mean values. 
J. Dorignac, Yu. B. Gaididei, J. C. Eilbeck, P. L. Christiansen, C.   Katerji