Dynamics of the double slit experiment

[gerald V]

The spatial orientation of the double slit setup be so that the screen extends in a plane ##x = constant##, while the entire apparatus sits on a ray perpendicular to the screen (of course, the slits sit and extend a bit off this ray).

My questions are about the dynamics in x-direction if only a single electron is involved. Is this more or less classical? That is: Makes it sense to say that the electron is emitted at a specific point in time (or how large is the uncertainty), and can this point in time be determined? The same for the impact of the electron on the screen? Can the flying time from emission from the source to impact on the screen be computed and/or measured and if yes, how does it depend on the diffraction angle?

Thank you in advance!

 

[vanhees71]

It depends on the state the electron is prepared in. The usual point of the double-slit experiment is however to demonstrate quantum behavior, and you describe an incoming electron running with a very well determined momentum perpendicular to the slits towards the slits (you can take a plane wave as an idealization). Then you solve the Schrödinger equation, using Huygens's principle, which leads to interference of the partial waves originating from each of the slit, i.e., if you look far enough from the slits, in the region, where these two partial waves overlap, you get interference fringes for the matter waves.

The meaning however is that the ##|\psi(x)|^2## is the position probability density for a single electron, i.e., each single electron running through the slits and hitting the screen will leave a single dot there. Repeating the experiment with very many equally prepared single electrons leads to a distribution of the dots given by the probability distribution predicted by the wave function.

For an excellent discussion of this issue, see the beginning of the Feynman Lectures, vol. III:

http://www.feynmanlectures.caltech.edu/III_01.html