I used to wonder exactly how Quantum Mechanics models the phenomenon of a single electron encountering a double slit and then being detected at a point which ends up as part of an interference pattern.
I'm now aware that solving the problem analytically is complicated: the electron has to be modelled as a suitable wavepacket, and the double slit as a potential barrier with gaps. However, the java applet here shows it all wonderfully.
The best setting for me is with a small slit-size (10) and with detector distance 50. Note the reflected part of the wavefunction is symmetrical with the transmitted part.
We're not seeing the wavefunction itself, but the modulus squared - the probability wave (mod(Ψ))2.