  We study the evolution of the most general initial Gaussian packet with
nonzero correlation coefficient between the coordinate and momentum operators
in the presence of a repulsive delta potential barrier, using the known exact
propagator of the time-dependent Schr\"odinger equation. For the initial packet
localized far enough from the barrier, we define the transmission coefficient
as the probability of discovering the particle in the whole semi-axis on the
other side of the barrier. It appears that the asymptotical transmission
coefficient (calculated in the large time limit) depends on two dimensionless
parameters: the normalized ratio of the potential strength to the initial mean
value of momentum and the ratio of the initial momentum dispersion to the
initial mean value of momentum. For small values of the second parameter the
result is reduced to the well known formula for the transparency of the delta
barrier, obtained in the plane wave approximation by solving the stationary
Schr\"odinger equation. For big values of the second parameter, the
transmission coefficient can be much bigger than that calculated in the plane
wave approximation. For a fixed initial spread of the packet in the coordinate
space, the initial correlation coefficient influences the transparency of the
barrier only indirectly, through the increase of the initial momentum
dispersion.
