Path Integral QM: Intro and Forward/Backward Scattering

[grzz]

hello

I started to read ‘QFT in a Nutshell’ by A. Zee. In the introduction to the path integral formulation of quantum mechanics there is the story about a particle going through a series of screens with holes drilled through them. Then the number of holes in each screen is increased. This results in the spaces on the screen which are not yet drilled becoming very small.
My difficulty is this. The undrilled spaces are then so small that they themselves may act as obstacles thereby providing an amplitude of scattering the particles backwards. Am I complicating things by including this backward scattering together with the amplitude of forward propagation of the paticle?
Any help?
Thanks.

 

[PeterDonis]

The undrilled spaces are then so small that they themselves may act as obstacles thereby providing an amplitude of scattering the particles backwards.

This is true even when the undrilled spaces are not small. For example, if we have a screen with a single hole, the entire rest of the screen has a nonzero amplitude of scattering the particle backwards.

Am I complicating things by including this backward scattering together with the amplitude of forward propagation of the paticle?

Yes, at least for the simple version Zee is considering at this point in the book. The key is that, in the example given, we are evaluating the amplitude for the particle to go from a particular source, which has some location in space, to a particular detector, which has some other location in space. We are not considering the amplitude for the particle to go somewhere else, such as being scattered backwards and flying off to a place where we don't even have a detector.

(And even more strictly, it should be "location in spacetime", not just "location in space"--i.e., we are evaluating the amplitude for the particle to be emitted from the source at some particular time and detected at the detector at some other particular time.)