Recent content by DoobleD

Thank you for answering. This is not super clear to me but I'll try to work on it.

Hi folks, I'm trying to get a grasp on some of the basic concepts of QFT. Specifically, I'm trying to picture what are the actual fields of QFT and how they relate to wavefunctions. There are already many helpful posts about those concepts, here and in other places, but some points are fuzzy...

Yes, I see no reason why it couldn't.

Yes, I am aware of what single slit diffraction patterns look like and what multiple slits interference patterns look like. I did study all of that. Though I am certainly no expert of it.

Right, I have used a bad terminology.

Look, I'm not speculating anything. What you wrote on post #17 is correct, and what I wrote is correct as well: if ##b >> \lambda##, the spread of the wave when it goes through the slit is too small to see, and you're eyes can't see any diffraction effect on the screen either because the fringes...

You'd only see smooth light evenly spread. The interferences are there I suppose (I should have used "appear" instead of "happen"), but you don't see it. It is too small. Like when sunlight goes through a window, you can't see any diffraction pattern because the width of the window is so much...

If ##\lambda << b## (the case where there are many "result wavelets" in the slit), what do you see on the diffraction screen ?

By diffraction I meant the fact that light spreads when it goes throught the slit. If there are say 10^10000 wavelets in the slit, it does not happen, and the diffraction pattern you are referring to does not appear in that case. EDIT : and by "wavelets" here I mean the end result that is the...

Yes but they do interfere to form ##n=l/\lambda## wavelets. That's what's represented in the images of the OP. The goal of this post is precisely to understand why in fine they are ##n=l/\lambda## "wavelets-like" sources in the slit, so that we get the diffraction behavior (if we didn't have...

Yep, I know. I am not asking about the diffraction pattern, I am looking at the wavelets themselves.

It seems I have made a mistake yesterday: the sum expression ##\sum_{i=0}^n\cos\left(x-i\cdot\frac{2\pi}{n}\right)## is apparently equal to ##cos(x)## (from Wolfram). So the correct integral form must be different than ##\int_0^L\cos\left(x-x'\right)dx'##, contrary to what I thought yesterday...

Ok, so that's what I suspected, and it does makes sense. Oh, ok. To check that I added a few cosines of same wavelength but out of phases and graphed the sum, indeed the result also has the same wavelength ! It makes sense visually, but I never realized that. So if I add infinitely many waves...

Thank you for answering ! Okay the behavior is going to be related to ##\lambda##, but that doesn't tell why there are specifically ##l/\lambda## wavelets in the slit. Huygens principle states that "every point on a wavefront is itself the source of spherical wavelets". So there should be...

Ok I' have tried some kind of simple analytical approach. Let's label the axis along the slit as ##x##, and define ##x = 0## at one end of the slit. Suppose we have infinitely many wavelets in the slit. Along the slit axis, that would give an infinite sum of, say, cosines, each slightly shifted...