Increase in amplitude of an electron wave

[SteveinLondon]

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.

 

[mathman]

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.

 

[Browne]

The wavefunction of a particle must satisfy the following condition:
$$\int_{-\infty}^{\infty} |\Psi|^2 dx = 1$$
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.

 

[San K]

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.

 

[SteveinLondon]

What does "probabilities normalized" mean?

 

[San K]

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...