(1) Mean kinetic energy of the incoming wave packet below the potential barrier

(2) Mean kinetic energy of the incoming wave packet corresponds approximately to the potential barrier

(3) Mean kinetic energy of the incoming wave packet above the potential barrier

Potentials can be found at which a wave packet is completely transmitted. Here is an example of a secant hyperbolic potential:

The wave packet is also completely transmitted in the inverted case.

Before you watch the next video, think about whether one of the wave packets will emerge as the winner in a "race", and if so, which one.