  The Mott-Hubbard transition is studied in the context of the two-dimensional
Hubbard model. Analytical calculations show the existence of a critical value
Uc of the potential strength which separates a paramagnetic metallic phase from
a paramagnetic insulating phase. Calculations of the density of states and
double occupancy show that the ground state in the insulating phase contains
always a small fraction of empty and doubly occupied sites. The structure of
the ground state is studied by considering the probability amplitude of
intersite hopping. The results indicate that the ground state of the Mott
insulator is characterized by a local antiferromagnetic order; the electrons
keep some mobility, but this mobility must be compatible with the local
ordering. The vanishing of some intersite probability amplitudes at U=Uc puts a
constrain on the electron mobility. It is suggested that such quantities might
be taken as the quantities which control the order in the insulating phase.
