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2:51 AM
I have thought about this some more.
What it comes down to in the end is: why does a particle whose
oops
Why does a particle whose state is described by psi(x) = exp(2pi i k x) have a definite momentum p = h*k?
Essentially the result comes from a combination of special relativity and the photoelectric effect.
Photoelectric gives us E = hf and special relativity gives us E = pc
Then you include the de Broglie hypothesis to extend it to matter
 

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