This applet shows a Gaussian wave packet squeezing through a slit. In addition to the pattern on the screen behind the slit one finds an - even more pronounced - interference pattern in the backwards direction. This phenomenon is known in classical wave theory as "backscattering".
First study the forward direction: What happens when the packet width s, the velocity v0 or the slit width d are changed? Compare this to the classical situation. Can you find a connection between changes of v0 and d? Please note: If you decrease s, the packet will spread rapidly. In order to see the effects of a narrow packet, you have to move it closer to the slit.
Now look at the backscattering, especially as a function of v0, and again compare it to a corresponding classical situation.