1.2 Mb MPEG movie of electron hitting infinitely hard wall
As you might be able to guess from the labels, this is a movie of the
electron probability density as a function of position. There are a couple
of features to notice about how the packet moves. The electron density
is a perfectly smooth Gaussian until there is nonzero probability for reaching
the wall. Once probability reaches the wall and starts reflecting, an oscillatory
structure emerges; this structure can be thought of as the interference
between the part of the wave function still travelling to negative x and
the part of the wave function that has reflected from the wall and is now
travelling to positive x. You should also notice in the movie that the
packet immediately starts getting wider and shorter: this effect is from
dispersion of the packet because the higher energy components of the packet
move faster than the lower energy components. A subtle effect that is difficult
to see in this movie is that the oscillitory structure has a shorter wavelength
when the packet is just starting to hit the wall than when the packet is
almost finished colliding with the wall; this is due to the same dispersion
mechanism: the higher energy components (short wave length) reach the wall
first and the lower energy components (longer wave length) reach the wall
later. Finally, notice that after the collision with the wall is completed
the packet is again a perfectly smooth Gaussian. Why?