What's the Force Acting on an Isolated Electron at (0,0,0)?

[eaglelake]

But then the particle states of which the waves are a superposition would need to be described in the position basis and once again would become a particle of waves. So the particle is a particle of waves of particles of waves of particles of waves...

Is it the chicken or the egg?

This is a common misconception - that somehow the particle is a wave, or a superposition of waves, This is not true! The fallacy occurs when we confuse the particle, which is a part of the experiment, with the state function, which is a mathematical thing that we use to determine probabilities. The state function is a probability amplitude defined in a linear function space. The state function does not describe the behavior of the particle as it traverses through the experimental apparatus. Nor does the state function propagate in 3-space, as the particle does. Particles interact with particle detectors, state functions do not. No experiment has ever revealed a state function moving along with the particle.

The quantum mechanical explanation of tunneling is thus: If the momentum state is an eigenstate of momentum, i.e. we have prepared particles with a known momentum, then there is an infinite uncertainty in the particles position. That means we have no idea where the particle will be found when we make a position measurement. The experimental results verify this. Position measurements find some particles in front of the barrier, while other measurements find it behind the barrier, as if it had somehow penetrated (tunneled?) through the barrier. But such a view is a classical picture that has no connection with the results of this experiment. All we know is that, in the tunneling experiment, some particles are found beyond the barrier, and with the state function, we can predict the probability of this happening. Neither quantum theory nor the actual experiment gives a mechanism for such behavior. There is no answer to the question, "how did the particle get beyond the barrier"? Quantum mechanics doesn't tell us, and we know classical mechanics doesn't work.
Best wishes

 

[meopemuk]

All we know is that, in the tunneling experiment, some particles are found beyond the barrier, and with the state function, we can predict the probability of this happening. Neither quantum theory nor the actual experiment gives a mechanism for such behavior. There is no answer to the question, "how did the particle get beyond the barrier"? Quantum mechanics doesn't tell us, and we know classical mechanics doesn't work.
Best wishes

This is exactly right. QM is not designed to provide mechanistic explanations of "why" and "how" things happen. QM is only a mathematical formalism that allows us to predict results of measurements.

The endless debates about "interpretations" of quantum mechanics and "is electron a particle or a wave?" cannot be resolved by scientific means. These debates result from unrealistic expectations that physics must give us detailed mechanisms of everything happening in nature, including things that happen when no observations are made. One can invent dozens of such mechanisms, including such bizarre ideas that the whole world splits into infinite number of copies once an electron touches a measuring device. These ideas cannot be checked by experiments, so they do not belong to science.

Feynman was right that one should not ask too many questions about QM. "Shut up and calculate!"

Eugene.

 

[ytuab]

Bohr's 1913 calculations are erroneous in many ways, as you know. He did not use Schrodinger's equation. Bohr's 1913 solution is not the same as Schrodinger's equation, which does gives the correct solution for the the Hydrogen atom.

You are correct: the reduced mass should be used. But, the significant thing here is that what we now call quantum mechanics uses Schrodinger's equation. The reduced mass, on the other hand, is not an essential concept in quantum mechanics. I am puzzled why you put so much emphasis on it.

The old quantum mechanics that existed prior to 1927 is now understood to be a mess that erroneously tried to modify classical mechanics to explain quantum events. Every new problem required ad hoc assumptions to make it work. We do ignore it today, because that is not how we do quantum mechanics. Today, when we say "quantum mechanics", it is understood to be 1927 and later.

eaglelake, SpectraCat, thanks for your reply.

But I think this thread is about "whether the force is influencing the momentum or not in QM".
You said "There is no force acting. Force is a classical concept." in #10.
Of cource I see what you mean. But the reduced mass is an essential concept in QM.
If you don't use the nuclear movement, the energy error would be greater than the relativistic energy error.
If you think the reduced mass is not related to the nuclear movement(this is the same as the electron movement), the equation of the reduced mass as I said above would not be obtained. Here I mean the electron movement is the classical rotaion or the classical oscillation by the classical force.

If we do $$m_{p} \to \infty$$, the reduced mass $$\frac{m_{e}m_{p}}{m_{e}+m_{p}} \to m_{e}$$. this means the reduced mass is related to the nuclear (or electron) movement.
Using only the QM methods or only the Coulomb potential (not force) we can't ariive at this equation of the reduced mass.

 

[LostConjugate]

Whew... well at least I proved my point that its not for fact a particle. I see your point about how a wave function in an infinite LVS is not the same as waves in 3-space. Will keep it in mind.

 

[SpectraCat]

eaglelake, SpectraCat, thanks for your reply.

But I think this thread is about "whether the force is influencing the momentum or not in QM".
You said "There is no force acting. Force is a classical concept." in #10.
Of cource I see what you mean. But the reduced mass is an essential concept in QM.
If you don't use the nuclear movement, the energy error would be greater than the relativistic energy error.
If you think the reduced mass is not related to the nuclear movement(this is the same as the electron movement), the equation of the reduced mass as I said above would not be obtained. Here I mean the electron movement is the classical rotaion or the classical oscillation by the classical force.

If we do $$m_{p} \to \infty$$, the reduced mass $$\frac{m_{e}m_{p}}{m_{e}+m_{p}} \to m_{e}$$. this means the reduced mass is related to the nuclear (or electron) movement.
Using only the QM methods or only the Coulomb potential (not force) we can't ariive at this equation of the reduced mass.

Look, reduced mass has NOTHING to do with QM or CM per se ... it is not somehow essential, as you seem to be making out to be. Yes, the H-atom levels are wrong if you don't take the finite mass of the nucleus into account ... why should that be surprising?

Reduced mass is simply a transformation to an inertial frame of reference that is more computationally convenient. It is probably possible to work out all of these solutions in an inertial frame where the motion of each particle is considered independently, but AFAIK nobody bothers to do that because it is WAY harder, and would anyway be equivalent to the known solutions using reduced mass.

 

[SpectraCat]

Whew... well at least I proved my point that its not for fact a particle. I see your point about how a wave function in an infinite LVS is not the same as waves in 3-space. Will keep it in mind.

Who said it was just a particle? I never did ... I said that experiments designed to measure particle properties do exactly that, and likewise for experiments designed to measure wave properties.

Another poster said it was a particle *with an associated probability wave*, which is just a casual description of the deBroglie-Bohm picture of Q.M., which is also completely consistent with available experimental evidence.

Oh .. and I also said, "An electron is neither a particle nor a wave, and it is both." ... which is a phrasing I came up with and like a lot, but probably has already been said by someone before me.