  Quantum theory of the intraband resonant tunneling of a Bose-Einstein
condensate loaded in a twodimensional optical lattice is considered. It is
shown that the phenomena of quantum collapse and revival can be observed in the
fully quantum problem. The mean-field limit of the theory is analyzed using the
WKB approximation for discrete equations, establishing in this way a direct
connection between the two approaches conventionally used in very different
physical contexts. More specifically we show that there exist two different
regimes of tunneling and study dependence of quantum collapse and revival on
the number of condensed atoms.
