Slits

Lets apply the many paths method to situations with slits.

Firstly lets consider 2 slits. The method can be used to calculate the probability that a photon arrives at any point on the screen. For each point there are 2 obvious paths.
When we do this we get an interesting result.

Bear in mind that this is NOT interference taking place. We are only considering ONE single photon. If the source were so dim that there was only one photon in existence at any time the pattern above would gradually build up. This experiment has been done and it does happen!

How about if we only have one slit?

Lets consider 3 paths which pass through 3 different points in the space of the slit. ( we call these waypoints )

You should be starting to see that this is quite a powerful model.