  We consider coherent tunneling of one-dimensional model systems in non-cyclic
or cyclic symmetric double well potentials. Generic potentials are constructed
which allow for analytical estimates of the quantum dynamics in the
non-relativistic deep tunneling regime, in terms of the tunneling distance,
barrier height and mass (or moment of inertia). For cyclic systems, the results
may be scaled to agree well with periodic potentials for which semi-analytical
results in terms of Mathieu functions exist. Starting from a wavepacket which
is initially localized in one of the potential wells, the subsequent periodic
tunneling is associated with tunneling velocities. These velocities (or angular
velocities) are evaluated as the ratio of the flux densities versus the
probability densities. The maximum velocities are found under the top of the
barrier where they scale as the square root of the ratio of barrier height and
mass (or moment of inertia), independent of the tunneling distance. They are
applied exemplarily to several prototypical molecular models of non-cyclic and
cyclic tunneling, including ammonia inversion, Cope rearrangment of
semibullvalene, torsions of molecular fragments, and rotational tunneling in
strong laser fields. Typical maximum velocities and angular velocities are in
the order of a few km/s and from 10 to 100 THz for our non-cyclic and cyclic
systems, respectively, much faster than time-averaged velocities. Even for the
more extreme case of an electron tunneling through a barrier of height of one
Hartree, the velocity is only about one percent of the speed of light.
Estimates of the corresponding time scales for passing through {the narrow
domain just} below the potential barrier are in the domain from 2 to 40 fs,
much shorter than the tunneling times.
