Conditions for Double-Slit Interference in Quantum Mechanics

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Robert_G
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Hi, there

Today, a friend came to me and asked the following questions and they made me confused.
If the source is strong, the light has to be considered as wave, and the double-slit interference (DSI) can be interpreted, and the conditions for the DSI is (1) same frequencies, (2) parallel polarization, and (3) constant phase differences.

If the source is week, one photon after one photon, for example. DSI will give us spots at the beginning; but give it a long time, the pattern will be formed.

Both of us never check it in the laboratory, we just read it from the book. However, In the "Quantum Mechanics" books, the above three conditions never be mentioned, As if those conditions does not mattered anymore.

In my opinion, All the three conditions are still needed. The character of frequency, polarization and phase difference are still with photons. Just look at the formulas of the creation and annihilation operators for the field. However, I can explain what the frequency, polarization and phase difference means to the particles (photons here), So I can not convince him, and my dear friend insists that those three conditions fade away in Quantum mechanics.

If we use the electrons in the DSI experiment, the coherent source is still need, right?

So, what you think?
 
on Phys.org
Dear me, I put my questions in the wrong place, here is classical physics, what should i do?