Increase in amplitude of an electron wave

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Discussion Overview

The discussion centers on the behavior of electron waves and their amplitude in relation to energy input, particularly in the context of wave/particle duality. Participants explore the implications of adding energy to electrons and photons, comparing it to classical wave behavior, and examining the mathematical properties of wavefunctions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions why the amplitude of an electron wave does not increase with added energy, suggesting that energy results in a reduction of wavelength instead.
  • Another participant notes that for photons, the situation can be more complex, as in lasers where amplitude can increase while frequency remains constant.
  • A participant explains that the wavefunction must satisfy a normalization condition, indicating that the total probability of finding a particle must equal one, and increasing amplitude would imply multiple particles.
  • There is a reiteration of the idea that the amplitude relates to probabilities rather than energy or frequency, emphasizing that the wavefunction is a mathematical construct rather than a physical wave.
  • Several participants seek clarification on the term "probabilities normalized," with one explaining that it refers to ensuring the total probability sums to one.
  • Another participant adds that a sum above one would imply a single particle appearing in multiple locations simultaneously.

Areas of Agreement / Disagreement

Participants express differing views on the nature of amplitude in relation to energy and probability, with no consensus reached on the implications of these concepts for electron and photon behavior.

Contextual Notes

The discussion includes assumptions about wavefunctions and normalization that may not be universally accepted or fully explored, leaving some mathematical steps and definitions unresolved.

SteveinLondon
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Like photons, all particles have a wave/particle duality, so when energy is added to an electron, say in a particle accelerator, why does the "amplitude" of the electron wave never increase (say as an increase in the actual number of electrons) - why is it that the energy added always just comes out in the form of a reduction in wavelength of the single electron, keeping the number of electrons at "1"? It seems to be the same with photons - whenever energy is added it's just the frequency that changes, never the amplitude/intensity, as would happen with a wave? For example - if we added energy to a water wave, it would get physically bigger - it's amplitude would increase.
 
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For photons it is more complicated, depending on how the energy is added. For example, in a laser the frequency stays the same, but the amplitude is increased.
 
The wavefunction of a particle must satisfy the following condition:
<br /> \int_{-\infty}^{\infty} |\Psi|^2 dx = 1<br />
Basically, this means that the total probability of finding the particle anywhere is one. It doesn't really make sense otherwise.

If you were to increase the amplitude of the wave by 2 everywhere, for example, the integral would be equal to 4. That essentially means there are now 4 particles.
 
SteveinLondon said:
Like photons, all particles have a wave/particle duality, so when energy is added to an electron, say in a particle accelerator, why does the "amplitude" of the electron wave never increase (say as an increase in the actual number of electrons) - why is it that the energy added always just comes out in the form of a reduction in wavelength of the single electron, keeping the number of electrons at "1"? It seems to be the same with photons - whenever energy is added it's just the frequency that changes, never the amplitude/intensity, as would happen with a wave? For example - if we added energy to a water wave, it would get physically bigger - it's amplitude would increase.

The amplitude is of probabilities (of locating photon) not frequency/energy. This "wave" is just a mathematical tool not any actual wave.

The probabilities as Browne suggests must equal one. However it does not have to be four particles, just one particle
with probabilities re-normalized.
 
What does "probabilities normalized" mean?
 
SteveinLondon said:
What does "probabilities normalized" mean?

the summation/integral brought back to one...

a sum above 1 would mean the same particle showing up at two places at the same time...
 
Last edited:

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