Increase in amplitude of an electron wave

In summary, particles, like photons, have a wave/particle duality and when energy is added to them, the amplitude of their wave does not increase. Instead, the energy is manifested as a reduction in wavelength. This is due to the fact that the wavefunction of a particle must satisfy a condition where the total probability of finding the particle anywhere is one. This means that increasing the amplitude of the wave would result in a sum above one, which is not physically possible. Therefore, the energy is distributed as a change in wavelength, rather than an increase in amplitude.
  • #1
SteveinLondon
10
0
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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  • #2
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.
 
  • #3
The wavefunction of a particle must satisfy the following condition:
[tex]
\int_{-\infty}^{\infty} |\Psi|^2 dx = 1
[/tex]
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.
 
  • #4
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.
 
  • #5
What does "probabilities normalized" mean?
 
  • #6
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:

Related to Increase in amplitude of an electron wave

1. How does increasing the amplitude of an electron wave affect its energy?

Increasing the amplitude of an electron wave does not directly affect its energy. The energy of an electron wave is determined by its frequency, not its amplitude. However, increasing the amplitude can impact the behavior and properties of the wave.

2. Can the amplitude of an electron wave be increased indefinitely?

No, the amplitude of an electron wave cannot be increased indefinitely. The amplitude is limited by the energy of the electron and the physical boundaries of the system it is in. There is a maximum amplitude that an electron wave can reach before it becomes unstable.

3. How does increasing the amplitude of an electron wave affect its wavelength?

Increasing the amplitude of an electron wave does not directly affect its wavelength. The wavelength is determined by the speed of the electron and its frequency. However, changing the amplitude can influence the electron's behavior and may indirectly impact the wavelength.

4. Does increasing the amplitude of an electron wave affect its probability of being in a certain location?

Yes, increasing the amplitude of an electron wave can affect its probability of being in a certain location. The amplitude of the wave determines the intensity of the electron's presence in a given location. Higher amplitudes indicate a higher probability of the electron being present in that area.

5. What factors can cause an increase in the amplitude of an electron wave?

An increase in the amplitude of an electron wave can be caused by factors such as the energy of the electron, the potential of the system it is in, and any external forces acting on the electron. Other factors, such as interference and superposition, can also influence the amplitude of an electron wave.

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