Wavelength of a Stationary Particle

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Discussion Overview

The discussion centers around the concept of the wavelength of a stationary particle, specifically in the context of the photoelectric effect and de Broglie wavelength. Participants explore the implications of an electron's wavelength approaching infinity as its velocity approaches zero, raising questions about the nature of particles and their momentum.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions what happens to the wavelength of an ejected electron when its velocity is zero, noting that the equation suggests the wavelength approaches infinity.
  • Another participant humorously suggests consulting Heisenberg for clarity on the matter, indicating uncertainty in the interpretation.
  • A participant references a related thread, suggesting that there may be additional insights available on the topic.
  • It is noted that the infinite wavelength corresponds to zero momentum, implying that the electron is not behaving as a wave and is not in motion, which is unusual for electrons.
  • One participant expresses frustration with repeated misconceptions about the nature of plane waves and their representation in quantum mechanics, emphasizing the implications of the Heisenberg uncertainty principle.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the wavelength and momentum relationship, with some agreeing on the implications of zero momentum while others contest the understanding of wave functions in quantum mechanics. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants highlight the limitations of classical interpretations when applied to quantum mechanics, particularly regarding the nature of momentum and the implications of the Heisenberg uncertainty principle.

Drakkith
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We were going over the basics of the photoelectric effect today in my solid state chemistry class when my instructor gave us a question asking what the wavelength of an ejected electron was. We worked through the question and got the answer, but that got me thinking.

If the wavelength is: λ=h/p, or λ=h/(mv), what happens when the velocity of the electron is zero? The equation seems to imply that the wavelength goes to infinity as v approaches zero. What's going on there?
 
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Drakkith said:
If the wavelength is: λ=h/p, or λ=h/(mv), what happens when the velocity of the electron is zero? The equation seems to imply that the wavelength goes to infinity as v approaches zero. What's going on there?
Ask Heisenberg. He knows, but he is not certain :wink:
 
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Thanks DC!
 
Thanks, @Greg Bernhardt , but DrClaude got it already. And besides, this is more of a deBroglie wavelength question rather than a photoelectric effect question.

But to add, when we look at the spectrum of the photoelectrons, we often look at the Energy versus momentum spectrum (E vs k). So already, there is a description of the wavelength of the photoelectrons. The λ=∞ simply means that there's zero momentum. It is not a wave and it is not moving, which for an electron, is highly unusual in most cases.

... and that reminds me, I really should finish my photoelectric effect article. Argh!

Zz.
 
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ZapperZ said:
The λ=∞ simply means that there's zero momentum. It is not a wave and it is not moving, ...
bold by me

Thanks for this. Now I understand what @Demystifier was getting at in his reply.
 
Again and again the same nonsense!

Plane waves (and for 0 momentum it's a constant!) are not representing states but are generalized functions living in the dual of the nuclear space (where the self-adjoint operators representing position and momentum are defined) of the rigged Hilbert space used in quantum theory. A particle cannot have an exactly sharp momentum. That's reflected by the Heisenberg uncertainty principle, ##\Delta x \Delta p_x \geq \hbar/2##.
 

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