Application of Heisenberg Uncertainty Principle

In summary, the electron has acquired momentum in the y direction and the uncertainty principle states that the momentum cannot be determined to an accuracy greater than Δpx.
  • #36
BvU said:
And we are into interpretation issues if we defend option 3 (##\approx##, formerly A:) which as Fowler works out, is true for the whole lot -- which is an even greater majority. The other two options (> and >>) can be ruled out.
BvU said:
The statement ##|p_y| \;d\ < \ h \ ## can be considered true for the electrons that end up in the central maximum, i.e. the majority. That central maximum has a width ##\Delta p_y \approx h/d ## which is the Heisenberg uncertainty relation (see Fowler).
---
Why these two statements are contradicting made by you.
In first one you are saying approx statement is for majority electrons
And in second you are saying (< ) statement is for majority?
 
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  • #37
I don't find them contradictory; why do you ?
 
  • #38
Means in first quote of you in post 36 you are saying,
|py|d ≈ h is true for majority electrons
and in second quote of you in post 36 you are saying,
|py|d < h is true for majority electrons?
 
  • #39
I see what you mean: in #32 ##\approx## I should have used the ##\Delta## instead of the | | for more clarity . (I did in #36).
Case can be made that both are true (difference between ##\Delta## and | | isn't that big), so no contradiction.
 
  • #40
Okay got it. That Δ and | | signs were creating confusion but not now.:smile:
I wonder, why tagging @Orodruin is not catching his attention even when I see him recently on some other thread.
 
  • #41
Raghav Gupta said:
I wonder, why tagging @Orodruin is not catching his attention even when I see him recently on some other thread.

I see it. I just do not have time to read through the thread on my breaks at work.
 
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  • #42
Twist in a tale then.
I think Hiesenberg uncertainty principle is irrelevant here after seeing this video.


Net is a wonderful thing to explore.
Got all of question and solution in this. But still why Hiesenberg gives diff. Answer and this method a different one?
About video, it is an Indian accent one but language is English. It is an approximately 1 minute video.
 
  • #43
Total hogwash ! Re-read Fowler to understand why; he mentions it explicitly.
 
  • #44
BvU said:
Total hogwash ! Re-read Fowler to understand why; he mentions it explicitly.
But Fowler is mainly talking about uncertainty.
Here in video, the guy is saying
By De- Broglie relationship ( as Fowler also says)
λ = h/p --- 1)
Then for diffraction, λ≈d ,
But we don't want diffraction , so d >> λ
Therefore d >> h/p
So pd >> h
So what is the hogwash here?
 
  • #45
Spelling it out (quoting Michael Fowler, Virginia univ):
we know from experiment that this is not what happens—a single slit diffraction pattern builds up, of angular width ##\ \theta \sim \lambda /w ## , where the electron’s de Broglie wavelength ##λ## is given by ##p_x \cong h/\lambda ## (there is a negligible contribution to ##λ## from the y-momentum). The consequent uncertainty in ##p_y## is

$$Δp_y/p_x \cong \theta \cong \lambda/w$$

Putting in ##p_x = h/\lambda ## , we find immediately that

$$\Delta p_y = h/λ$$
I can't put it into words any better than that

--
 
  • #46
BvU said:
Spelling it out (quoting Michael Fowler, Virginia univ):

I can't put it into words any better than that

--
That is correct,
Δpy=h/λ
Then how the term d will be introduced?
 
  • #47
That is what I have written in post 44,
λ = h/p
Manipulating,
p = h/λ
 
  • #48
Connect the dots: Fowler's w is your d.
 
  • #49
BvU said:
Connect the dots: Fowler's w is your d.
Yeah, got it from that
Δpyd ≈ h , thanks.
But I should admit
2 mistakes
First from the answer key of our paper
And then from the video solution. :mad:
 
  • #50
I'm pretty convinced the answer ##\ |p_y|\;d \ < \ h\ ## is actually correct
 
  • #51
BvU said:
I'm pretty convinced the answer ##\ |p_y|\;d \ < \ h\ ## is actually correct
:oldsurprised:
Haha,
You were saying the other thing previously.
 
  • #52
Are we back to posts 32, 35, 36 and have to go the loop again ?
 
  • #53
BvU said:
Are we back to posts 32, 35, 36 and have to go the loop again ?
Yeah, I think
There is confusion between two options
|py|d < h
|py |d ≅ h
 
  • #54
BvU said:
Are we back to posts 32, 35, 36 and have to go the loop again ?
Sorry for the post 53, it was non sensible.
Can you tell, if we have got from fowler Δpyd ≈h
Then how | py| d < h ?
I have seen posts 32,35,36 carefully now.
You are saying this is not good exercise but anyways I am interested.
 
  • #55
BvU said:
(difference between ##\Delta## and | | isn't that big)
This statement was also a bit confusing from you for me
As I replaced Δpyd ≈h
To |py|d ≈h
Because you are saying difference between these two signs are not big.
 
  • #56
Raghav Gupta said:
Sorry for the post 53, it was non sensible.
Can you tell, if we have got from fowler Δpyd ≈h
Then how | py| d < h ?
I have seen posts 32,35,36 carefully now.
You are saying this is not good exercise but anyways I am interested.
The central maximum in the diffraction pattern from a single slit has a width Δpy ≈ h / d (see Fowler). Most electrons end up in the central maximum, so for most electrons | py| d < h

I am having a bit of a deja vu feeling now.
 
  • #57
Okay, got it but not completely.
I have not read diffraction so much. I guess I have to know some very basic concepts first to understand whole of the fowler.
Will search myself for the moment.
Thanks by the way.
 
  • #58
You're welcome. Don't forget #32: don't spend too much energy on this. It'll come by a few more times later on in the curriculum in different incarnations.
 
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