  We consider the Klein-Gordon equation on two half-axes connected at their
origins. We add a potential that is constant but different on each branch. In a
previous paper, we studied the L-infinity-time decay via H\"ormander's version
of the stationary phase method. Here we apply these results to show that for
initial conditions in an energy band above the threshold of the tunnel effect a
fixed portion of the energy propagates between group lines. Further we consider
the situation that the potential difference tends to infinity while the energy
band of the initial condition is shifted upwards such that the particle stays
above the threshold of tunnel effect. We show that the total transmitted energy
as well as the portion between the group lines tend to zero like the inverse of
the square root of the higher potential in the corresponding branch if this
potential tends to infinity. At the same time the cone formed by the group
lines inclines to the t-axis while its aperture tends to zero.

Analysis of PDEs