Math of Electron Double Slit Experiment

[Ghost Quartz]

I'm looking for a good derivation of the "wave" patterns in this experiment. I suppose that if wave-particle duality is an obsolete idea, there must be a derivation from quantum mechanics that gets close results.
Thanks in advance

 

[PeroK]

There was a thread recently called "Is wave-matter duality a proven theory" which involved a discussion about this, with some links.

That might be interesting.

 

[vanhees71]

How familiar are you with the description of diffraction in classical electrodynamics/optics? In nonrelativistic QT it's almost the same theory, based on the Helmholtz equation and the corresponding Green's function given the boundary conditions due to the slits.

An alternative also pretty intuitive way is the use of the path integral. This is nicely worked out in the book by Feynman and Hibbs.

 

[DrChinese]

You may find this treatment useful:

https://arxiv.org/abs/quant-ph/0703126

 

[Ghost Quartz]

the link posted by DrChinese is what I was looking for. Thank you, everyone!