Possible Paths and Interference Patterns in the Double Slit Experiment

[San K]

Does "all possible paths", per fenyman, mean (say in a single particle double slit):

Slit a & b
or does it mean
slit a & b plus slit a plus slit b

how is the interference pattern calculated?

also when we try to get which way :
Could we say that now some of the paths now are no longer possible/valid and hence no interference pattern?

 

[Fredrik]

It means that the probability of detection at a given location is calculated by adding the amplitude associated with the path through A (from the emitter to the given location) to the amplitude associated with the path through B, and then taking the square of the absolute value of the result.

I recommend the book "QED: The strange theory of light and matter" by Richard Feynman, and the videos of the lectures that this book is based on.

The interference pattern could in principle be calculated this way, but I suspect that it's easier to just solve the Schrödinger equation for the two-slit problem. I have never calculated it myself though.