What Is the Shape of a Free Electron Wave?

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Discussion Overview

The discussion centers on the shape of a free electron wave, exploring whether it resembles a sinusoidal plane wave like electromagnetic waves, and how it behaves in different contexts such as the double slit experiment and various electron sources like electron guns and particle accelerators.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Jake questions whether a free electron wave is a sinusoidal plane wave and if it expands laterally like an EM wave, suggesting that the double slit experiment supports this idea.
  • Some participants propose that any linear combination of plane waves with different frequencies and wave vectors is a solution to the free Schrödinger equation, with the actual solution depending on the electron source.
  • There is interest in the specific shapes of electron waves produced by standard electron emitters or guns and particle accelerators.
  • One participant notes that to achieve a "plane" wave, one must be far from the source and may need to limit the flux with a diaphragm, asserting that wave properties apply to electrons as well.
  • Another participant states that electrons in an accelerator exhibit well-defined momentum and energy, approximating them as plane waves, with corrections being negligible for measurements relevant to quantum mechanics.

Areas of Agreement / Disagreement

Participants express interest in the topic and share similar inquiries about electron wave shapes and sources, but there is no consensus on the exact nature of the electron wave or its representation.

Contextual Notes

Limitations include the dependence on specific definitions of wave shapes and the conditions under which different electron sources operate. The discussion does not resolve the complexities of how electron waves manifest in various experimental setups.

Who May Find This Useful

Readers interested in quantum mechanics, wave-particle duality, and experimental physics may find this discussion relevant.

jaketodd
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What is the shape of a free electron wave? Is it a sinusoidal plane wave like an EM wave? Does it expand laterally like an EM wave? I'm thinking the answers to these questions is yes because the double slit experiment works for electrons. But I'm not totally sure.

Thanks!

Jake
 
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Any linear combination of plane waves with different frequencies and wave vectors will be also a solution to the "free" Schroedinger equation. Actual solution is determined with the electron source (preparation device).
 
Bob_for_short said:
Any linear combination of plane waves with different frequencies and wave vectors will be also a solution to the "free" Schroedinger equation. Actual solution is determined with the electron source (preparation device).

So what are the possible shapes and electron sources? In particular, I'm interested in the shape of an electron wave from a standard electron emitter/gun (if there is a standard one) and from a particle accelerator.

Thank you!
 
Im interested in this question as well!
 
jaketodd said:
So what are the possible shapes and electron sources? In particular, I'm interested in the shape of an electron wave from a standard electron emitter/gun (if there is a standard one) and from a particle accelerator.
Thank you!

I am not an experimentalist. Think of electron wave as of a usual wave from some source. To obtain a "plane" wave you have to be far from the source, maybe limit the flux with some diaphragm, etc. I want to say that all the wave properties are applicable to the electron case.

A particle accelerator uses diaphragms so behind a diaphragm you have some plane wave with small diffraction due to the ratio (electron de Broglie wave-length)/(diaphragm width).
 
In particular, I'm interested in the shape of an electron wave from a standard electron emitter/gun (if there is a standard one) and from a particle accelerator.

The electrons in an accelerator have a well-defined momentum (and energy) , and so they are in momentum eigenstates to a good approximation, which means that they are plane waves [itex]\psi = e^{i \vec{k} \cdot \vec{x}}[/itex], especially on the length scales relevant for scattering in QM. The corrections which would arise by not treating the electrons as a plane wave are too small to be conceivably measured.
 

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