  A complete one-dimensional scattering of a spinless particle on a
time-independent potential barrier is considered. To describe separately
transmitted and reflected particles in the corresponding subsets of identical
experiments, we introduce the notions of scattering channels for transmission
and reflection. We find for both channels the (unitary) scattering matrices and
reconstruct, by known out asymptotes (i.e., by the transmitted and reflected
wave packets), the corresponding in asymptotes. Unlike the out asymptotes for
transmission and reflection, their in asymptotes represent nonorthogonal
functions. As is shown, the position distributions of to-be-transmitted and
to-be-reflected particles, except their average positions, are unpredictable.
At the same time, the momentum distributions of these particles are physically
meaningful and can be observed to the full. We show that both the subensembles
of particles must start (on the average) from the same spatial point, and the
momentum distributions of to-be-scattered and scattered particles must be the
same for each scattering channel. Taking into account these properties, we
define the (individual) delay times for transmission and reflection for wave
packets of an arbitrary width. Besides, to estimate the duration of the
scattering event, we derive the expression for a (total) scattering time.
