  It is shown that in the case of the one-particle one-dimensional scattering
problem for a given time-independent potential, for each state of the whole
quantum ensemble of identically prepared particles, there is an unique pair of
(subensemble's) solutions to the Schr\"odinger equation, which, as we
postulate, describe separately transmission and reflection: in the case of
nonstationary states, for any instant of time, these functions are orthogonal
and their sum describes the state of all particles; evolving with constant
norms, one of them approaches at late times the transmitted wave packet and
another approaches the reflected packet. Both for transmission and reflection,
1) well before and after the scattering event, the average kinetic energy of
particles is the same, 2) the average starting point differs, in the general
case, from that for all particles. It is shown that for reflection, in the case
of symmetric potential barriers, the domain of the motion of particles is
bounded by the midpoint of the barrier region. We define (exact and asymptotic)
transmission and reflection times and show that the basic results of our
formalism can be, in principle, checked experimentally.
