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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<h2>1. What is the Heisenberg Uncertainty Principle?</h2><p>The Heisenberg Uncertainty Principle, also known as the Uncertainty Principle, is a fundamental principle in quantum mechanics that states that it is impossible to know both the precise position and momentum of a subatomic particle at the same time.</p><h2>2. How does the Heisenberg Uncertainty Principle apply to real-world applications?</h2><p>The Heisenberg Uncertainty Principle has been applied in various fields, such as quantum cryptography, where it is used to ensure secure communication by preventing eavesdropping. It is also used in medical imaging, where it helps to improve the resolution of images by limiting the uncertainty in the position of particles. Additionally, it has been used in the development of sensitive instruments like atomic clocks and electron microscopes.</p><h2>3. Can the Heisenberg Uncertainty Principle be violated?</h2><p>No, the Heisenberg Uncertainty Principle is a fundamental principle of quantum mechanics and cannot be violated. It is a consequence of the wave-particle duality of subatomic particles and is supported by numerous experimental evidence.</p><h2>4. How does the Heisenberg Uncertainty Principle impact our understanding of the physical world?</h2><p>The Heisenberg Uncertainty Principle challenges our traditional understanding of the physical world, which is based on classical mechanics. It introduces the concept of uncertainty and probability, highlighting the inherently unpredictable nature of subatomic particles. It also plays a crucial role in the development of quantum mechanics and our understanding of the behavior of particles at the quantum level.</p><h2>5. Is there a mathematical equation for the Heisenberg Uncertainty Principle?</h2><p>Yes, the Heisenberg Uncertainty Principle is mathematically represented by the following equation: ΔxΔp ≥ h/4π, where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and h is the Planck constant. This equation quantifies the trade-off between the precision of measuring a particle's position and momentum, illustrating the uncertainty principle.</p>

1. What is the Heisenberg Uncertainty Principle?

The Heisenberg Uncertainty Principle, also known as the Uncertainty Principle, is a fundamental principle in quantum mechanics that states that it is impossible to know both the precise position and momentum of a subatomic particle at the same time.

2. How does the Heisenberg Uncertainty Principle apply to real-world applications?

The Heisenberg Uncertainty Principle has been applied in various fields, such as quantum cryptography, where it is used to ensure secure communication by preventing eavesdropping. It is also used in medical imaging, where it helps to improve the resolution of images by limiting the uncertainty in the position of particles. Additionally, it has been used in the development of sensitive instruments like atomic clocks and electron microscopes.

3. Can the Heisenberg Uncertainty Principle be violated?

No, the Heisenberg Uncertainty Principle is a fundamental principle of quantum mechanics and cannot be violated. It is a consequence of the wave-particle duality of subatomic particles and is supported by numerous experimental evidence.

4. How does the Heisenberg Uncertainty Principle impact our understanding of the physical world?

The Heisenberg Uncertainty Principle challenges our traditional understanding of the physical world, which is based on classical mechanics. It introduces the concept of uncertainty and probability, highlighting the inherently unpredictable nature of subatomic particles. It also plays a crucial role in the development of quantum mechanics and our understanding of the behavior of particles at the quantum level.

5. Is there a mathematical equation for the Heisenberg Uncertainty Principle?

Yes, the Heisenberg Uncertainty Principle is mathematically represented by the following equation: ΔxΔp ≥ h/4π, where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and h is the Planck constant. This equation quantifies the trade-off between the precision of measuring a particle's position and momentum, illustrating the uncertainty principle.

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