Probability and double slit

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I think you have a few misconceptions here. You start by talking about the particles in the beam "not interfering with each other" so the "wave function of each particle is lambda/p".

There are at least two problems with this statement. I'll take the last part first. It looks like you are confusing "wave function" with "wave length". The wave function doesn't have a value. It is a function. In a case like this we would write it as a function of position and particle momentum. We would find this function by solving the Schrodinger equation, but let's not get into how that is done.

Next is not useful to think of the particles "interfering" with each other. A wave function of a single particle "interferes with itself" but wave functions of different particles don't interfere with each other. The wavefunction of each particle needs to be solved for from the Schrodinger equation. Without going into gory detail about how that is done, it depends on what the interactions are with the rest of the system (in this case, interactions with the slits and with the other particles).

Essentially your question is "why do the slits affect the wavefunctions of the particles but the other particles don't". There are two answers:

  1. Typically the distances between particles in the beam are so large that the interactions between the particles are very weak and can be neglected.

  2. Even if the interactions are not very weak (a very high intensity beam) then each particle in the beam has many particles around it (in all directions). Typically, these particles are all charged. For sake of argument let's say that they are electrons. So they all repel each other. But that means that the repulsion due to all of the nearby electrons will tend to cancel out and once again, at least for most of the electrons, we can ignore the interactions.

An accelerator physicist could answer this better, but I'm guessing that reason 1. is more important most of the time.

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Updated on August 01, 2022

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  • seeker
    seeker over 1 year

    if a beam of identical particles at random distances from each other (or exactly 1/2 lambda between each other) travelling with the same v towards a double sllit do not interfere with each others wave function, so that the wave function of each particle upon reaching the double slit is always lambda / p, thus producing a predictable interference pattern,

    how come the wave function of the region BETWEEN the slits DOES interact with the wavefunction of each particle so as to 'block' (or greatly reduce) it so that each particle's wave function can interfere with ITSELF via the two slits?

    conversely, since the wavefunction of one particle (the inter-slit 'substance') can and seemingly does affect the wavefunction of another 'particle' (that of the approaching particle), why don't the particles in a beam interfere with each other so as to randomoly destroy any assignable wavelength to them?

    if the inter-slit region had no affect on the wavefunctions of the approaching particles, the diffraction grating / double slit apparatus would be entirely transparent to the beam and there would be no interference at all.

    The probability function is an entirely mathematical construct, and yet how it evolves over space must be dependent on whether there is any 'matter' in the region through which it passes. Is there something like a "damping factor" of freespace, for the probability function, like electrical permitivity of freespace?