HUP and the Double-Slit Experiment

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referframe

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Consider the following double-slit experiment: The source is an optical laser. The beam is, say, ½-inch wide and the laser is located far enough, say 10 yards, from the 2 slits to guarantee a large uncertainty in position (because of the very small uncertainty in the momentum direction). Obviously, the half-inch wide beam must cover the 2 slits.

I believe the above experiment would produce the classic interference pattern.

Now imagine moving the laser source closer and closer to the 2 slits so that the uncertainty in the momentum direction slowly increases. Would there be some point (distance between laser source and the 2 slits) at which the interference pattern would disappear because the experimental setup would no longer guarantee a large uncertainty in position?

As always, thanks in advance.
 

Nugatory

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As long as both slits are illuminated and we'll have an interference pattern.

It is generally best to calculate the pattern using the methods of wave mechanics. The uncertainty principle is baked into the mathematical formalism of the wave equation; invoking it directly here is primarily a way of satisfying ourselves that the calculated behavior is physically reasonable.
 

vanhees71

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Well, here you don't need quantum theory. Classical electrodynamics will do fine. A laser emits a pretty nice coherent wave-train you can treat as a plane wave for this purpose. The most simple approximation is Kirchhoff's theory of refraction. Exact solutions of the Maxwell equations, including all boundary conditions and polarization is pretty tough. For the half-plane it has been solved first by Sommerfeld (in his habilitation thesis if I remember right). Sommerfeld's lecture notes are a good source, but the optics volume is a particular gem!
 

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