  A {\it completed} scattering of a particle on a static one-dimensional (1D)
potential barrier is a combined quantum process to consist from two elementary
sub-processes (transmission and reflection) evolved coherently at all stages of
scattering and macroscopically distinct at the final stage. The existing model
of the process is clearly inadequate to its nature: all one-particle
"observables" and "tunneling times", introduced as quantities to be common for
the sub-processes, cannot be experimentally measured and, consequently, have no
physical meaning; on the contrary, quantities introduced for either sub-process
have no basis, for the time evolution of either sub-process is unknown in this
model. We show that the wave function to describe a completed scattering can be
uniquely presented as the sum of two solutions to the Schr\"odinger equation,
which describe separately the sub-processes at all stages of scattering. For
symmetric potential barriers such solutions are found explicitly. For either
sub-process we define the time spent, on the average, by a particle in the
barrier region. We define it as the Larmor time. As it turned out, this time is
just Buttiker's dwell time averaged over the corresponding localized state.
Thus, firstly, we justify the known definition of the local dwell time
introduced by Hauge and co-workers as well by Leavens and Aers, for now this
time can be measured; secondly, we confirm that namely Buttiker's dwell time
gives the energy-distribution for the tunneling time; thirdly, we state that
all the definitions are valid only if they are based on the wave functions for
transmission and reflection found in our paper. Besides, we define the exact
and asymptotic group times to be auxiliary in timing the scattering process.
