Double slits separation & electron field size

[Varon]

Supposed you want to send an electron to a double slit. What must be the separation of the slits if they are say 1 meter away?

What is the size of the initial electron field? When it travels to the slits, does the electron field expand in size? Why?

I'm asking this because I'd like to know if the initial electron field emitted from the emitter can become larger than the slits separation when it reach the slits.

Schrödinger preferred the pictures of waves representing particles but Lorentz made him realized that waves can spread. How come Schrödinger didn't think in terms of field that naturally spread (if it does)?

Note in this message I simply wanted to understand the field extend and behavior of the electron, not the behavior of the wave function. Thanks.

 

[Nugatory]

Assuming that when you say "the electron field" you mean the probability of finding the electron at a given point... the electron field spreads out to infinity and therefore you can place the slits as far apart as you wish. However, the farther away you go, the lower the probability of function nding the electron there will be. So in practice if you position the slits too far away and out of the high probability region (which is where your electron gun is pointing) most of the electrons will miss the slits and be absorbed by the barrier; the pattern on the screen will be undetectably weak because you just don't have enough electrons coming through.

Thus when we're designing these experiments we want to position the slits close enough to where we're aiming that we can get an easily detectable pattern.