Which wave function and operator is responsible for the Double Slit Experiment?

[curtdbz]

I know this may be a completely stupid question and it's so fundamental but... As we all know the first thing we learn is basically the duality between waves and particles (e.g electron). This is shown via the double slit experiment.

Now I know how to explain it if it were water waves, and using Huygen's equations, etc. But in quantum mechanics we have a wave function $$\psi$$ and an operator $$A$$, and using Schroedinger's equation we obtain the eigenvalues and THAT is what the result should be.

So how does one explain the results of the double slit experiment using that model? Which operator specifically (and what wave function) is in play? Thanks for helping me! I hope this question makes sense.

 

[curtdbz]

Just wondering if anyone knows..?

 

[Talisman]

There's a nice paper on arXiv that explains exactly this question. I'll try to find it (I don't know why I don't have a perma-link somewhere, since I searched many years for such a paper myself

(FWIW, I recall it simply claiming that the particle was in a superposition of two momentum eigenstates after the slit, and that the screen was measuring position... but that sounds too simplistic.)

[Edit: found it http://arxiv.org/pdf/quant-ph/0703126]

 

[curtdbz]

There's a nice paper on arXiv that explains exactly this question. I'll try to find it (I don't know why I don't have a perma-link somewhere, since I searched many years for such a paper myself

(FWIW, I recall it simply claiming that the particle was in a superposition of two momentum eigenstates after the slit, and that the screen was measuring position... but that sounds too simplistic.)

[Edit: found it http://arxiv.org/pdf/quant-ph/0703126]

Wow. Thanks so much, I really appreciate it!

PS: This may be another simple question but looking the paper it predicts (obviously) that there's zero probability of a particle being on the dips of the wave. However, whenever one looks at images of this experiment done with Photons (for ex.) there's always a few little dots where the theory predicts there should be None. Why is this? Noise? Lack of ideal conditions? If so, is there a way to alter the wave function or our predictions so that it correctly predicts the amount of photons that will appear in the 'dips'? Thanks again!

 

[Talisman]

Wow. Thanks so much, I really appreciate it!

PS: This may be another simple question but looking the paper it predicts (obviously) that there's zero probability of a particle being on the dips of the wave. However, whenever one looks at images of this experiment done with Photons (for ex.) there's always a few little dots where the theory predicts there should be None. Why is this? Noise? Lack of ideal conditions? If so, is there a way to alter the wave function or our predictions so that it correctly predicts the amount of photons that will appear in the 'dips'? Thanks again!

I must admit I understand this stuff very little myself, but from what I do understand: the basic idea is lack of ideal conditions. The more "which-path" information the apparatus gathers, the less interference is exhibited. This is not an all-or-nothing, and there may be some recoverable correlations in the system.

But alas, it is best if you wait for an answer from a more authoritative source than me