Dual particle and dual double slit interference

[San K]

In short the question I am trying to answer is:

1. do the "waves-functions" from separate particle interfere?

2. do the Schrödinger equations predict the interference pattern caused by the interference of the "wave functions" of two separate particles?

The above question is illustrated/clarified below in the form of an experimental setup:

we have two double slits placed side by side and a particle for each of the double slits traveling at same time.

lets say we have an experimental setup where we have a single particle (photon/electron) headed for double slits (labelled A1 & A2).

Now we create another double slit setup exactly similar as above. The double slits, in this case, are labelled B1 & B2.

We start bringing the double slits close to each other. close enough that the "wave function" emerging from, say, A2 can interfere with the "wave function" emerging from, say, B1.

Case 1: the single particle headed for double slits A1 and A2 is a photon
the single particle headed for double slits B1 and B2 is also a photon

Case 2: Case 1: the single particle headed for double slits A1 and A2 is a photon
the single particle headed for double slits B1 and B2 is an electron

 

[mfb]

1. do the "waves-functions" from separate particle interfere?

Possible, depends on the situation.

2. do the Schrödinger equations predict the interference pattern caused by the interference of the "wave functions" of two separate particles?

If you use the correct wave functions: Yes.

Case 1: the single particle headed for double slits A1 and A2 is a photon
the single particle headed for double slits B1 and B2 is also a photon

With two independent photon sources you won't see interference effects. But if you can guarantee that the photons have a fixed phase relation then you get interference.

Case 2: Case 1: the single particle headed for double slits A1 and A2 is a photon
the single particle headed for double slits B1 and B2 is an electron

Then you will detect one photon and one electron, independent of each other.