The electron as a wave: what is it that waves

[carwe]

The electron as a wave: what is it that "waves"

When taking a course in Modern Physics, after doing quite a lot of thinking, I finally asked the lecturer: when the elctron behaves as a wave, what kind of wave does it behave as? Does it behave as an electromagnetic wave? The answer was no. I thought for a second an asked, "Is it the probability that waves"? The lecturer thought for some moments and then aswered "yes".

Or, in other words, my question is: what does the oscillating variable describe? For an em wave it is obvious, it is the magnitude of the electric or magnetic field. So, when describing the electron as a wave, is it still so?

No, acording to the lecturer, which makes sense; we e.g. calculated the wave function for an electron-in-a-box, clearly; the wave appears and it is apparently the probability that "waves".

...but, in that case: when an em wave behaves as a particle, a photon, can that photon also be described as a "probability wave", different from the em wave?

Can someone give me some hints on this? I might very well be messing up a lot of things...

Thanks.

 

[haael]

I thought for a second an asked, "Is it the probability that waves"? The lecturer thought for some moments and then aswered "yes".

No, to be precise. It's the quantum phase that waves (the thing that is responsible for the double-slit pattern). The probability is the squared amplitude of that wave, but it is possible for it to be constant, so the probability is not "waving", while the phase still does.

The only thing that comes to mind with "waving probability" is the superposition of particles with different masses, i.e. neutrinos or neutral kaon.

Or, in other words, my question is: what does the oscillating variable describe? For an em wave it is obvious, it is the magnitude of the electric or magnetic field. So, when describing the electron as a wave, is it still so?

It's nothing but the electron field. Not the electromagnetic field, but the electron field. Note that fermion fields are a bit different from boson fields.

...but, in that case: when an em wave behaves as a particle, a photon, can that photon also be described as a "probability wave", different from the em wave?

No, it can't, which is a flaw in QM, IMO.

 

[kolabaum]

What "waves" is really the mathematical construction of the quantum state. Take a particle in a box as an example; by solving the stationary S.E you get wave functions that are superpositions of two waves traveling in opposite directions. Of course, the physical interpretation of the solutions are found by taking the absolute square of the wave functions - the "waves" are left as mathematical building blocks.

 

[Edgardo]

In some experiments the electron behaves like a wave:

1) http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/davger2.html#c1"
You shoot electrons at a crystal and observe an interference pattern. The pattern can be explained if you assume that the electron has a wavelength.

2) http://www.perimeterinstitute.ca/Perimeter_Explorations/Quantum_Reality/Chapter_2_-_Wave-Particle_Duality_with_Electrons/"
(Chapter 2, Perimeter Institute for Theoretical Physics)
You observe dots on the screen but the pattern looks as if produced by wave interference.