  The new method for the simulation of nonstationary quantum processes is
proposed. The method is based on the tomography representation of quantum
mechanics, {\it i.e.}, the state of the system is described by the {\it
nonnegative} function (quantum tomogram). In the framework of the method one
uses the ensemble of trajectories in the tomographic space to represent
evolution of the system (therefore direct calculation of the quantum tomogram
is avoided). To illustrate the method we consider the problem of nonstationary
tunneling of a wave packet. Different characteristics of tunneling, such as
tunneling time, evolution of spatial and momentum distributions, tunneling
probability are calculated in the quantum tomography approach. Tunneling of a
wave packet of composite particle, exciton, is also considered; exciton
ionization due to the scattering on the barrier is analyzed.
