Waveform of an electron

[altsci]

For example diffraction pattern of electron beam on MgO poly-crystalline . DeBroglie wave is a property of both the electron and the target. On energy I agree that photon will need energy. It is not impossible to pick up this energy from the atom of the target. What is important is that: DeBroglie wave can not be the property of only electron (velocity is always relative).

[swansont]

For example diffraction pattern of electron beam on MgO poly-crystalline . DeBroglie wave is a property of both the electron and the target.

How does h/p depend on the target? Is the wavelength different if the target is silicon?

 

On energy I agree that photon will need energy. It is not impossible to pick up this energy from the atom of the target. What is important is that: DeBroglie wave can not be the property of only electron (velocity is always relative).

Yes, I think it's basically impossible. The energy I chose is 6.25 keV. Somehow it picks up more than 70 keV of additional energy from a stationary target. That's not going to happen. (thermal energy is not an issue, being much less than an eV)

 

Yes, velocity is relative. That makes it frame dependent, not target dependent. There doesn't need to be a target.

[altsci]

Suppose in a chosen frame there are 2 targets and one and the same source of the electrons. Suppose the target #1 is stationary, but the target #2 receding from the source at grate speed. Will the diffraction pattern be the same? You will claim the same. Now change the frame to where the target #2 at rest...

[swansont]

Suppose in a chosen frame there are 2 targets and one and the same source of the electrons. Suppose the target #1 is stationary, but the target #2 receding from the source at grate speed. Will the diffraction pattern be the same? You will claim the same. Now change the frame to where the target #2 at rest...

 

 

As I said, it's frame dependent; the pattern will be determined by the values in the rest frame of the target. That's not the same as being target dependent. The latter is a poor use of terminology. The former is utterly unsurprising.

[altsci]

If one has the one sours of electrons and 2 moving targets - one has 2 frames where the first target at rest and the second target at rest. The velocity of the electron that goes to DeBroglies formula will be different in those frames. So, the frequency will be target dependent.

[swansont]

If one has the one sours of electrons and 2 moving targets - one has 2 frames where the first target at rest and the second target at rest. The velocity of the electron that goes to DeBroglies formula will be different in those frames. So, the frequency will be target dependent.

 

Frame dependent. Velocity is a condition of the frame. Saying target dependent implies it's due to an intrinsic property of the target, and velocity is not an intrinsic property of the target.

[Phi for All]

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Moderator Note

Posts hijacking this topic with a non-mainstream declaration that DeBroglie's formula is not correct have been split off to here.

[Enthalpy]

The equation of motion of the electron in a potential field is set by the boundary conditions, not the electron charge or mass.

 

Ouch.

[Enthalpy]

Ahum. Maybe I can make a better answer than a single word.

 

The equation of motion of the electron in a potential field is set by the boundary conditions, not the electron charge or mass.

 

The potential field results from some interaction with the electron, which is often an electric potential because an electron is most sensitive to it due to its charge, and is in most cases the electric potential from nuclei and other electrons. But for simplicity, said potential is often modelled as an energy of undefined nature, with some distribution over space - like a tub for a quantum well, a ring for a benzene molecule.

 

Then the equation for the electron gives a set of solutions where the rest mass and the kinetic energy don't necessarily appear as such, depending on how you decide to write them.

 

Among these solutions, some depend on the time only by exp(j2pi*Et/h). Their amplitude is constant over time. They're called "stationary", and are indeed immobile, static, motionless and so on - except that the electron can have a kinetic energy, a momentum, an angular momentum. So ol' Schrödinger's equation not only describes the movements of electrons, but also immobile electrons.

 

Stationary solutions are useful because where the electron is confined in one or few atoms, the energies associated with the varied stationary solutions are well separated, especially as compared with kT at room temperature, and then the usual case is that the electrons in the well fill the modes of lowest energy and leave the others unused, with certainty.

 

As well, we know that when an electron is trapped, all the possible wavefunctions are linear combinations of the stationary solutions. And here we see moving wavefunctions, that do evolve over time, just as combinations of immobile solutions.

 

Take a 1-D nanowire as an example. The first stationary solution is a half-wave (with certain boundary conditions) and the second a full wave over the length, with a phase exp(j2pi*E₁t/h) and exp(j2pi*E₂t/h). When the wave is a superposition of both, like 1/sqrt(2) of each, say during the emission or absorption of a photon, the superposition reinforces the wave at one half of the nanowire at some times and weakens the other, and at other times it reinforces the other half. This results from both waves of the superposition being in phase or in opposition.

 

The phase condition evolves with time because both phases rotate, with frequencies E₁/h and E₂/h. A reinforcing superposition at one nanowire half happens again with a frequency of (E₁-E₂)/h. As the resulting wave isn't stationary, the electron has a movement, in this case from one nanowire half to the other, with that frequency (E₁-E₂)/h, at which it also emits or absorbs light because of the accelerating charge.

 

And now we see the mass appear, because E₁ and E₂ depend on it through E=(hk/2pi)²/(2m) where the nanowire length sets possible values of k, and so does (E₁-E₂)/h, the frequency of the electron's movement.