Exploring Electron Motion in Quantum Mechanics

[ZIKA99]

TL;DR Summary

Reverse electron motion ?

I had two questions in the field of physics:
We know that in quantum mechanics there is an electron in a certain distance from the distance to the nucleus as a cloud or a cover. But is motion for the cloud defined by the electron moving around the nucleus?
And the main question is, can the motion of the electron be reversed?
For this question you consider all electron theories.
If my answer is not clear, tell me again.

 

[PeroK]

Summary:: Reverse electron motion ?

I had two questions in the field of physics:
We know that in quantum mechanics there is an electron in a certain distance from the distance to the nucleus as a cloud or a cover. But is motion for the cloud defined by the electron moving around the nucleus?
And the main question is, can the motion of the electron be reversed?
For this question you consider all electron theories.
If my answer is not clear, tell me again.

Electrons bound to a nucleus are not described by classical equations of motion. Instead, each electron is described by four quantum numbers: Energy, total angular momentum, magnetic moment, and spin. The last two have signed values, so the magnetic moment can be $\pm m$, where $m = 0, 1, 2 \dots$ and the spin can be $\pm \frac 1 2$. That is analagous to classical clockwise and anti-clockwise orbits and spins.

 

[phinds]

can the motion of the electron be reversed?

What would that even mean?

 

[ZIKA99]

What would that even mean?

That is, if an electron rotates in a certain direction around the nucleus, can it move in the opposite direction (electron) with anything?
If it has an unknown movement, write it down.

 

[PeroK]

That is, if an electron rotates in a certain direction around the nucleus, can it move in the opposite direction (electron) with anything?
If it has an unknown movement, write it down.

When an electron shell is full, then the electrons between them have all possible combinations of orbital angular momentum and spin. That represents the QM equivalent of orbits in both directions (clockwise and anti-clockwise).

It's worth re-emphasising, however, that electrons are not orbiting the nucleus in classical trajectories. So, any question about "in what directions are they moving?" is meaningless.

 

[ZIKA99]

When an electron shell is full, then the electrons between them have all possible combinations of orbital angular momentum and spin. That represents the QM equivalent of orbits in both directions (clockwise and anti-clockwise).

It's worth re-emphasising, however, that electrons are not orbiting the nucleus in classical trajectories. So, any question about "in what directions are they moving?" is meaningless.

Excuse me, can you explain more?
And what does this sentence prove?
My main point is whether they have ever been able to reverse the motion of an electron, either theoretically or experimentally, that is, if it rotates clockwise, it is counterclockwise (the same electron). ) To rotate.
If the motion of electrons around the nucleus is meaningless, then is there no motion for electrons around the nucleus?

 

[PeroK]

Excuse me, can you explain more?
And what does this sentence prove?
My main point is whether they have ever been able to reverse the motion of an electron, either theoretically or experimentally, that is, if it rotates clockwise, it is counterclockwise (the same electron). ) To rotate.
If the motion of electrons around the nucleus is meaningless, then is there no motion for electrons around the nucleus?

The point is that electrons in an atom are not moving - not in any classical sense. The atom is a QM system and cannot be described in the terms of classical motion.

 

[PeterDonis]

My main point is whether they have ever been able to reverse the motion of an electron

This question cannot be answered because it is based on a false premise, that "the motion of an electron" in an atom is classical motion that can be "reversed". It isn't. Quantum mechanics does not work the same as classical mechanics, and your intuitions from classical mechanics will not work when you try to apply them to quantum objects like electrons in atoms.

If the motion of electrons around the nucleus is meaningless, then is there no motion for electrons around the nucleus?

The very concept of "motion of electrons around the nucleus" is meaningless, because, as above, electrons in atoms aren't classical objects and your intuitions about classical objects do not apply to them. It is like asking what color the number three is; "color" isn't even a concept that applies to numbers, and similarly, classical "motion" isn't even a concept that applies to electrons in atoms.

 

[PeterDonis]

The point is that electrons in an atom are not moving - not in any classical sense.

I would not use the phrase "are not moving", because that implies that the term "moving" makes sense when applied to electrons in atoms. It is like saying that the number three is not blue--that doesn't really convey the fact that "color" is not even a concept that applies to numbers. Similarly, "moving" is not even a concept that applies to electrons in atoms, so any sentence that involves "electron" and "moving" is meaningless, even the sentence you wrote, that electrons in atoms are not moving.

 

[ZIKA99]

Thank you for your explanation. If you have another opinion, write it.

 

[PeterDonis]

Thank you for your explanation. If you have another opinion, write it.

I'm not sure what you mean by "another opinion". First, what I have posted is not an opinion, it's an experimental fact. Second, if you mean explain how electrons in atoms actually behave, that's way too broad for a PF thread; you need a college level course in quantum mechanics or the equivalent in personal study time.

 

[ZIKA99]

I'm not sure what you mean by "another opinion". First, what I have posted is not an opinion, it's an experimental fact. Second, if you mean explain how electrons in atoms actually behave, that's way too broad for a PF thread; you need a college level course in quantum mechanics or the equivalent in personal study time.

I meant that if you have a more complete explanation of this topic, write it down.
If you have a book on quantum theory, introduce it.
sincerely

 

[vela]

I meant that if you have a more complete explanation of this topic, write it down.

How much more complete of an explanation can you get than "your question is meaningless"?

 

[ZIKA99]

How much more complete of an explanation can you get than "your question is meaningless"?

As far as I think no question in science has been meaningless.
I have to say that if you read the story of scientists, they have all started with meaningless questions, not self-definition, but because even the most meaningless and ridiculous questions in science are worth thinking about.
If you understand, he will not say a word.

 

[WernerQH]

I think it's an extreme position to say that electrons in an atom don't move, or that the idea is meaningless. After all there is a velocity operator, and there is kinetic energy, which is definitely not zero. It is true that one must not think of trajectories; positions and velocities are defined only in statistical sense. But it is moving electrons that do the radiating, and you can express the emission probability in terms of the velocity correlations.

 

[berkeman]

I meant that if you have a more complete explanation of this topic, write it down.
If you have a book on quantum theory, introduce it.
sincerely

As far as I think no question in science has been meaningless.
I have to say that if you read the story of scientists, they have all started with meaningless questions, not self-definition, but because even the most meaningless and ridiculous questions in science are worth thinking about.
If you understand, he will not say a word.

https://en.wikipedia.org/wiki/Quantum_mechanics

 

[PeroK]

 

[PeterDonis]

I meant that if you have a more complete explanation of this topic, write it down.

As I have already said, that would be way too much for a PF thread.

If you have a book on quantum theory, introduce it.

I personally think Ballentine would be a good textbook to start with.

 

[vanhees71]

I meant that if you have a more complete explanation of this topic, write it down.
If you have a book on quantum theory, introduce it.
sincerely

You have to forget all what you learned about the atom in terms of the Bohr-Sommerfeld old quantum theory. It's outdated since 1925 and shouldn't be taught except in lectures on the history of quantum theory (I recommend the huge work by Mehra and Rechenberg).

It is an observational fact that a (non-radioactive atom) is very stable, i.e., once put somewhere not interacting too energetically with anything else around it, will stay in its ground state (state of lowest energy) forever. That means it's in a time-independent state. In the lingo of formal QT we say it's in an energy eigenstate. The energy eigenstates are precisely the stationary states, describing a situation where nothing changes with time.

What one has get used to when entering the quantum realm is that observables like position or momentum don't take determined values except if the system were prepared in a state such that this is certain (and the quantum formalism tells you that this is impossible due to the Heisenberg-Robertson-Schrödinger uncertainty relation for position and momentum). All quantum theory describes are the probabilities for getting a value of an observable when measuring it given the system's state it is prepared in.

For an electron indide an atom you get a probability distribution for finding it at some position when measured. The same holds for momentum. To get an idea about the momentum of an electron when prepared in an energy eigenstate of an atom, you can ask for the expectation value. The quantum formalism tells you that the expectation value is 0. So on average the electron is indeed not moving.

To be in a stationary state is important for our understanding why matter is stable, and this is for me the most convincing argument for the invalidity of classical physics when describing matter. If the electron where really moving in some orbit around the nucleus as envisaged in the outdated old quantum theory a la Bohr and Sommerfeld, it should radiate electromagnetic radiation and thus loose energy and finally crash into the nucleus. Nothing like this is fortunately the case, because according to the new quantum theory, valid with utmost precise confirmation by experiments, the electron is not moving in such a naive sense but is in a stationary state, i.e., an energy eigenstate, of the atom.

The only honest half-popular book about quantum theory I know is the corresponding volume in Susskind's "Theoretical Minimum" series. There's no way to understand quantum theory without math, and Susskind provides indeed the minimum needed to starting to really understand quantum theory.

 

[WernerQH]

The energy eigenstates are precisely the stationary states, describing a situation where nothing changes with time.
[...]
To get an idea about the momentum of an electron when prepared in an energy eigenstate of an atom, you can ask for the expectation value. The quantum formalism tells you that the expectation value is 0. So on average the electron is indeed not moving.

The "electron cloud" is not moving. But this should not be taken to mean that the electrons making up the cloud are at rest. As you surely know, the square of the velocity (momentum) operator has a non-zero expectation value. The situation is not unlike that of a volume of air that is in equilibrium (stationary!): the molecules flit about at (roughly) the speed of sound.

 

[PeroK]

The "electron cloud" is not moving. But this should not be taken to mean that the electrons making up the cloud are at rest. As you surely know, the square of the velocity (momentum) operator has a non-zero expectation value. The situation is not unlike that of a volume of air that is in equilibrium (stationary!): the molecules flit about at (roughly) the speed of sound.

If you really believe in QM, then you have to stop trying to analyse whether an electron is "at rest" or not. Classical concepts require classical trajectories. The electron does not not have a time dependent position in the first place. It may, however, have a time-dependent expectation value of position: although in a stationary state the expectation value of position (and all observables) is time independent.

These woolly arguments that "the electron is not at rest because ..." reveal a lack of disciplined thinking and mathematical precision.

We do not say a question is meaningless in order to evade an answer; but, in order to maintain a discipline of thought that reflects the mathematical model underpinning the QM atom.

 

[AndreiB]

The point is that electrons in an atom are not moving - not in any classical sense.

This is an unjustified assertion. We do not know if the electrons move or not, we do not even know what an electron is. It's also difficult to make sense about a stationary object having a momentum.

The atom is a QM system and cannot be described in the terms of classical motion.

There is no reason to believe such an assertion. A classical atomic model is discussed in this paper:

Relativity and Radiation Balance for the Classical Hydrogen Atom in Classical Electromagnetic Zero-Point Radiation​

Timothy H. Boyer
European Journal of Physics 42, 025205(22) (2021)

The model is far from perfect, but it is, if you like, an existence proof. A classical atom can be stable under certain conditions.

 

[WernerQH]

These woolly arguments that "the electron is not at rest because ..." reveal a lack of disciplined thinking and mathematical precision.

We do not say a question is meaningless in order to evade an answer; but, in order to maintain a discipline of thought that reflects the mathematical model underpinning the QM atom.

I agree with you that the arguments are woolly. I'd prefer not to talk about "electrons". But what am I to do when I want to be understood? Electrons are neither particles nor waves, but have features of both. How do you "maintain a discipline of thought" when the basic concepts are contradictory? I don't believe in electrons. Expositions of quantum (field) theory should not be based on such concepts, but on currents (events).

 

[AndreiB]

To be in a stationary state is important for our understanding why matter is stable, and this is for me the most convincing argument for the invalidity of classical physics when describing matter. If the electron where really moving in some orbit around the nucleus as envisaged in the outdated old quantum theory a la Bohr and Sommerfeld, it should radiate electromagnetic radiation and thus loose energy and finally crash into the nucleus.

This assumes the atom is alone in the universe, no fields around it. Once this assumption is dropped, classical atoms may be possible. Indeed, a classical atom cannot be in a static equilibrium but it can be in a dynamical one.

 

[PeroK]

I agree with you that the arguments are woolly. I'd prefer not to talk about "electrons". But what am I to do when I want to be understood? Electrons are neither particles nor waves, but have features of both. How do you "maintain a discipline of thought" when the basic concepts are contradictory? I don't believe in electrons. Expositions of quantum (field) theory should not be based on such concepts, but on currents (events).

There are no contradictions in QM. Electrons are particles, by definition. Contradictions only appear when you you insist on using terms in their classical context.

 

[ZIKA99]

I am familiar with quantum mechanics, only its formulations and mathematics are difficult for me.
Thank you for your explanation.

 

[PeroK]

I am familiar with quantum mechanics, only its formulations and mathematics are difficult for me.
Thank you for your explanation.

And I'm familiar with the Russian language, only its words and phrases are difficult for me!

 

[ZIKA99]

And I'm familiar with the Russian language, only its words and phrases are difficult for me!

I'm sorry, I use a translator, so sometimes it translates badly.
By familiarity with quantum mechanics, I mean the definitions that exist in this field, but I do not know any of the proofs in mathematical language in this field. This means that I want to enter the mathematical calculations of quantum mechanics.
I am acquaintance with quantum mechanics, only its formulation and mathematics are difficult for me.
Thank you for your explanation.

 

[Ian J Miller]

It seems to me that if we look at the equation as Schrödinger actually first wrote it there is a kinetic energy term, a potential energy term, and it is consistent with a Lagrangian underpinning. Therefore, for motion is a central field (a) there are two degrees of freedom, and the electron moves with a kinetic energy -V/2, V the potential energy (from the virial theorem) Accordingly there is at least half a quantum of orbital angular momentum as n = (nr + 1/2) + (ℓ + 1/2). (A semiclassical reference: Schiller (1962), Phys Rev 125 1100. An additional reason for accepting this is that if there is no angular motion, it would violate the Uncertainty Principle because in an external frame of reference you would know an orientation of the line between the electron and nucleus, and it would have zero angular motion.) It looks like an electron cloud because, from the Hellmann Feynman theorem the net electric field is that of an electrostatic distribution equal to the probability distribution of electron location.

A more interesting question is why does the Stern Gerlach experiment not show a magnetic moment for the s electron? My explanation is wave motion is circular in nature, thus if you put a cork on the sea, as the waves go by, it describes circular motion but stays in the same place. This, of course, sits better with a pilot wave type interpretation which most will not like. Sorry about that. But if that is correct, in answer to the original question, yes, it can go both ways and does so every period. Of course the radial component does this anyway. And no, this makes little sense in terms of classical trajectories, but I don't think anyone believes in classical trajectories.

 

[PeterDonis]

My explanation is

Please review the PF rules on personal speculation. At best, this kind of thing belongs in the QM interpretations forum, not this one. But even there you need to be careful about personal speculation.

As far as basic QM is concerned, your statements are not correct.