  The modeling of the early universe is done through the quantization of a
Friedmann-Robertson-Walker model with positive curvature. The material content
consists of two fluids: radiation and Chaplygin gas. The quantization of these
models is made by following the Wheeler and DeWitt's prescriptions. Using the
Schutz formalism, the time notion is recovered and the Wheeler-DeWitt equation
transforms into a time dependent Schr\"{o}dinger equation, which rules the
dynamics of the early universe, under the action of an effective potential
$V_{ef}$. Using a finite differences method and the Crank-Nicholson scheme, in
a code implemented in the program OCTAVE, we solve the corresponding time
dependent Schr\"{o}dinger equation and obtain the time evolution of a initial
wave packet. This wave packet satisfies appropriate boundary conditions. The
calculation of the tunneling probabilities shows that the universe may emerge
from the Planck era to an inflationary phase. It also shows that, the tunneling
probability is a function of the mean energy of the initial wave packet and of
two parameters related to the Chaplygin gas. We also show a comparison between
these results and those obtained by the WKB approximation.
