As individual photons strike a photographic plate after passing through a double slit they appear to strike randomly. As more and more photons strike the plate, the diffraction pattern emerges. Photons strike the plate according to a probability function.
When we look at a single photon passing through the double slit, we can only talk about the probability of where it will strike the film. It has a greater probability of striking the film where the intensity of the interference pattern is large. It has very little probability of striking the film where the intensity of the interference pattern is small. For a single photon, we can refer to the deBroglie wave as a wave of probability. The electric wave has amplitude E and its intensity S is proportional to the square of that amplitude,
In a similar manner the deBroglie wave has amplitude we label (a capital Greek letter "psi") and the probability P of finding the photon at some place is proportional to the square of that amplitude,
This is true in general, for electrons or for any particles. Now we must describe situations in terms of probabilities.
When a single photon passes through the double slit we can no longer predict exactly where it will hit the film. This is quite different from throwing a baseball at a wall with two windows in it! The behavior of tiny particles does not correspond to our common everyday experiences!
Complementairity Uncertainty Return to Ch 28, Quantum Mechanics (c) Doug Davis, 2002; all rights reserved