How diffraction of a wave through a aperture in terms of the uncertain

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Discussion Overview

The discussion explores the qualitative relationship between the diffraction of a wave through an aperture and the uncertainty principle, particularly in the context of light passing through a single slit.

Discussion Character

  • Exploratory, Conceptual clarification, Technical explanation

Main Points Raised

  • One participant describes how reducing the size of a slit increases the certainty of a photon’s position, leading to greater uncertainty in its momentum, as expressed by the uncertainty principle (Δx)(Δp) = ħ.
  • This participant notes that as the slit becomes smaller, the light diffracts more, indicating a relationship between aperture size and diffraction effects.
  • Another participant questions whether this treatment leads to a sinc(x) distribution, suggesting a connection to wave theory and its agreement with experimental measurements.
  • A later reply acknowledges the use of wave approaches in calculations while relating them to the uncertainty principle, indicating a synthesis of concepts.

Areas of Agreement / Disagreement

Participants express varying degrees of understanding and interpretation of the relationship between diffraction and the uncertainty principle, with no clear consensus on the implications of the calculations or the specific outcomes.

Contextual Notes

Some assumptions about the relationship between slit size, diffraction patterns, and the uncertainty principle remain unexamined, and the discussion does not resolve the mathematical implications of the proposed models.

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How could you describe qualitatively how diffraction of a wave through a aperture in terms of the uncertainty principle?


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lets take a single slit and shine light through it . If i make this slit smaller and force the light to go through it , i know to much about the position of the photons they must be though that opening (delta x) so now i must get an uncertainty in the momentum of the photons , so (dx)(dp)=(h-bar) , When i make the slit to small the light starts to spread out and diffract .
The smaller i make the slit the more uncertainty i will have in the photons momentum .
I don't know if this is what you were looking for .
 


Thank you, much appreciated.
 


cragar said:
lets take a single slit and shine light through it . If i make this slit smaller and force the light to go through it , i know to much about the position of the photons they must be though that opening (delta x) so now i must get an uncertainty in the momentum of the photons , so (dx)(dp)=(h-bar) , When i make the slit to small the light starts to spread out and diffract .
The smaller i make the slit the more uncertainty i will have in the photons momentum .
I don't know if this is what you were looking for .

Does that treatment yield a sin(x)/x distribution? Wave theory does- and it agrees with measurement very well.
 
Last edited by a moderator:


Oh I see, now. Interesting. The calculations do, in fact, seem to use a wave approach to get actual values but relate it to uncertainty. Fair enough - it's always useful to tie things together.
 

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