  A time-dependent multiconfigurational self-consistent field theory is
presented to describe the many-body dynamics of a gas of identical bosonic
atoms confined to an external trapping potential at zero temperature from first
principles. A set of generalized evolution equations are developed, through the
time-dependent variational principle, which account for the complete and
self-consistent coupling between the expansion coefficients of each
configuration and the underlying one-body wave functions within a restricted
two state Fock space basis that includes the full effects of the condensate's
mean field as well as atomic correlation. The resulting dynamical equations are
a classical Hamiltonian system and, by construction, form a well-defined
initial value problem. They are implemented in an efficient numerical
algorithm. An example is presented, highlighting the generality of the theory,
in which the ballistic expansion of a fragmented condensate ground state is
compared to that of a macroscopic quantum superposition state, taken here to be
a highly entangled number state, upon releasing the external trapping
potential. Strikingly different many-body matter-wave dynamics emerge in each
case, accentuating the role of both atomic correlation and mean-field effects
in the two condensate states.
