# B Do electrons accelerate when transitioning from one energy state to another?

#### Iceking20

Summary
Do electrons accelerate when they absorb or emit energy?
Do electrons have motion or they just accelerate when they get enough energy?

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Staff Emeritus
Your question is very unclear. More precisely, you have one question in your title, a different one in the summary and a third in the body of your message. What is your exact question?

#### Nugatory

Mentor
Summary: Do electrons accelerate when they absorb or emit energy?
Do electrons have motion or they just accelerate when they get enough energy?
For bound electrons (the ones that move from one energy state to another in an atom) it makes no sense to talk about their position, speed, or acceleration. The classical idea that the electron is some small object moving around the nucleus just doesn’t work in the quantum mechanical description.

#### Delta2

Homework Helper
Gold Member
Summary: Do electrons accelerate when they absorb or emit energy?

Do electrons have motion or they just accelerate when they get enough energy?
Yes the electrons have continuous motion if that's what you mean. Thus we can have position vector, velocity vector and acceleration vector assigned to an electron.

However according to the laws of quantum physics , which currently is our best theory for the behavior of microscopic particles like electron, we cannot determine their position vector and their velocity vector or their acceleration vector(like we do for a classical particle with the help of Newton's laws or with Euler-Lagrange equations).

The best we can do is assign a wave function $\psi(\vec{r},t)$ and with the help of schrodinger equation (or other similar equations that involve the wave function) to determine the wave function. Then the quantity $|\psi(\vec{r},t)|^2$ gives us the probability that the electron will be at an infinitesimal volume centered at position $\vec{r}$ at time $t$.

#### PeterDonis

Mentor
the electrons have continuous motion if that's what you mean. Thus we can have position vector, velocity vector and acceleration vector assigned to an electron.
This is only true if we are treating the electron classically. In some contexts (for example, electrons in a cathode ray tube) this can be a useful approximation, but it is only an approximation.

according to the laws of quantum physics , which currently is our best theory for the behavior of microscopic particles like electron, we cannot determine their position vector and their velocity vector or their acceleration vector
That's not what quantum mechanics says. It is not correct to think of an electron in an atom, for example, as having a definite position but we don't know what it is (so we have to use its wave function to predict probababilities).

#### Delta2

Homework Helper
Gold Member
This is only true if we are treating the electron classically. In some contexts (for example, electrons in a cathode ray tube) this can be a useful approximation, but it is only an approximation.
I don't understand. In quantum physics the electron is a point particle (true or false?). So it arises the question how does it move? Does it move like a point particle along a curved path (mith multiple zig zags e.t.c) which we just cant determine (because we don't have yet the appropriate theory) and so we can speak only with probabilities about its location and movement? Or what does it hold about the movement of electron in the regime of quantum physics?

#### PeterDonis

Mentor
In quantum physics the electron is a point particle (true or false?).
As you are using the term "point particle", this is false.

how does it move?
QM does not treat the electron as a point particle with a definite motion. So this question is meaningless and does not have a well-defined answer.

For bound electrons (the ones that move from one energy state to another in an atom) it makes no sense to talk about their position, speed, or acceleration. The classical idea that the electron is some small object moving around the nucleus just doesn’t work in the quantum mechanical description.
I might be interpreting your answer incorrectly but there seems to be a contradiction in what you wrote:

You refer to bound electrons as moving "from one energy state to another"

In other words you seem to be saying that the electrons move and that would suggest there we can talk about position speed and acceleration, for example the most probable position of an electron changes as a result of moving between energy states.

#### Nugatory

Mentor
You refer to bound electrons as moving "from one energy state to another"
That word could have been “change” or “transition”. There’s no more physical movement involved than when someone “moves” from one political party to another, or when public sentiment “shifts” on an issue, or a video game player “moves” to the next level.

#### DarMM

Gold Member
I don't understand. In quantum physics the electron is a point particle (true or false?). So it arises the question how does it move? Does it move like a point particle along a curved path (mith multiple zig zags e.t.c) which we just cant determine (because we don't have yet the appropriate theory) and so we can speak only with probabilities about its location and movement? Or what does it hold about the movement of electron in the regime of quantum physics?
Due to the Kochen-Specker and other no-go theorems we know that if an electron really has a definitive position then it's either communicating with its past self in some manner or it can influence other particles faster than light.

QM itself is completely silent on the issue and does not refer to electron trajectories at all.

#### Demystifier

2018 Award
Summary: Do electrons accelerate when they absorb or emit energy?

Do electrons have motion or they just accelerate when they get enough energy?
As others told you, this question does not make much sense within standard QM. But it makes perfect sense within Bohmian formulation of QM, in which case the answer is - fundamental particles have motion and accelerate. There are, however, reasons to think that electron may not be a fundamental particle (see the paper linked in my signature), in which case motion and acceleration should not be associated with electrons but with some more fundamental particles.

That word could have been “change” or “transition”. There’s no more physical movement involved than when someone “moves” from one political party to another, or when public sentiment “shifts” on an issue, or a video game player “moves” to the next level.
Sorry but I don't understand. Would you please clarify further? :

Suppose a hydrogen atom in the ground state became ionised. Are you saying that there is nothing equivalent to change of position and therefore movement during the event?

I understand that in some interpretations of QM concepts involving movement may be irrelevant but does QM and any interpretations of it forbid movement?

One of my sticking points here is related to the concept of probability. This seems to allow the electron to change location within energy levels as well as between energy levels. But, also, this seems to imply that the electron is something like a particle, a point particle perhaps, a concept which is rejected here. In light of this what is meant by statements of the type:

The most probable separation between the electron and proton in the ground state hydrogen atom is equal to the Bohr radius.

Thank you.

QM itself is completely silent on the issue and does not refer to electron trajectories at all.
This makes sense. I think.

As others told you, this question does not make much sense within standard QM. But it makes perfect sense within Bohmian formulation of QM, in which case the answer is - fundamental particles have motion and accelerate. There are, however, reasons to think that electron may not be a fundamental particle (see the paper linked in my signature), in which case motion and acceleration should not be associated with electrons but with some more fundamental particles.
So it seems that different interpretations of QM come up with different answers.

Staff Emeritus
Iceking posted an unclear message, and refused to clarify it. Thirteen messages later, we're still trying to figure out what he meant.

The question is "why"?

#### PeterDonis

Mentor
Suppose a hydrogen atom in the ground state became ionised. Are you saying that there is nothing equivalent to change of position and therefore movement during the event?
There is no definite position, velocity, or trajectory for the electron.

does QM and any interpretations of it forbid movement?
The math of QM says what I said above. Interpretations like Bohmian mechanics talk about "positions", but these positions are unobservable.

In light of this what is meant by statements of the type:

The most probable separation between the electron and proton in the ground state hydrogen atom is equal to the Bohr radius.
That the radial part of the ground state wave function for the electron in the hydrogen atom, in the position representation, has a peak at that radius.

There is no definite position, velocity, or trajectory for the electron.

The math of QM says what I said above. Interpretations like Bohmian mechanics talk about "positions", but these positions are unobservable.

That the radial part of the ground state wave function for the electron in the hydrogen atom, in the position representation, has a peak at that radius.
Thanks. I will respond to your three points separately:

1. I concur with what you wrote but I was enquiring about "change of position". Is there anything in QM that disallows changes of position, albeit that these changes are not definite. I think that when the atom is excited or ionised the most probable separation between the proton and electron increases. I think this is widely accepted and obvious. But is this not the case... can the maths of QM be interpreted as predicting that the separation doesn't happen? Is the concept of such changes not relevant to the maths of QM?

2. In some respects I concur again but I think the observations we do have, for example from excitation and de excitation events, provide some evidence that the separation between the proton and electron does change.

3. It seems that your answer is a paraphrase of the statement I made. Are the electron and proton best described in terms of mathematics and things such as peaks in wave functions. If so I'm wondering if such descriptions can accommodate measured properties such as charge.

Thank you.

#### PeterDonis

Mentor
I was enquiring about "change of position". Is there anything in QM that disallows changes of position, albeit that these changes are not definite.
If there is no definite position, there is no definite change of position.

I think the observations we do have, for example from excitation and de excitation events, provide some evidence that the separation between the proton and electron does change.
No, they provide evidence that the energy of the electron changes. None of these measurements involve measurements of position, so they tell us nothing about position or changes in position.

Are the electron and proton best described in terms of mathematics and things such as peaks in wave functions.
How else would you describe them and still make correct predictions about experimental results?

As Richard Feynman once said, "quantum mechanics was not wished upon us by theorists". Physicists did not make up all this math about wave functions just for funsies. They were forced to do it in order to make correct predictions about experimental results involving atoms and subatomic particles. Nobody has found any other way to do that; that's why QM is still our best current theory for describing such things.

I'm wondering if such descriptions can accommodate measured properties such as charge.
Measurements of charge are basically measurements of energy: how much energy a given charged particle picks up or loses as it passes through an EM field with particular defined properties.

If there is no definite position, there is no definite change of position.

No, they provide evidence that the energy of the electron changes. None of these measurements involve measurements of position, so they tell us nothing about position or changes in position.

How else would you describe them and still make correct predictions about experimental results?

As Richard Feynman once said, "quantum mechanics was not wished upon us by theorists". Physicists did not make up all this math about wave functions just for funsies. They were forced to do it in order to make correct predictions about experimental results involving atoms and subatomic particles. Nobody has found any other way to do that; that's why QM is still our best current theory for describing such things.

Measurements of charge are basically measurements of energy: how much energy a given charged particle picks up or loses as it passes through an EM field with particular defined properties.
Sorry but I'm getting the impression that you're not reading my comments properly. I would like to point out that I'm not disputing your comments about nothing being definite. Nor am I questioning the validity of QM.

1. You say there is no definite change of position. Accepted. But is there a change of position, albeit indefinite?

When the hydrogen atom is ionised does the does the most probable separation between the proton and electron increase?

That's the main thing I want to know

2. I agree that the energy of the atom changes but this energy can be equated, in part, to the change of potential energy of the atom, in other words to the separation between the proton and electron.

3. I agree with the descriptions and accept that QM is a very powerful theory. It seems that I might have given the opposite impression. All I want to know here is does the mathematical description accommodate measured properties. If so a reference would be useful.

4. In certain versions of Millikan's experiment charge is measured by observing charged oil drops which are either at rest or moving with constant velocity in a uniform electric field. I don't think energy measurements come into it but then I'm not (yet) familiar with more modern methods of measuring e.

Thank you

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#### Jehannum

If you think of an atomic electron as a probability amplitude, i.e. a possibility wave, then it's feasible to picture the change of orbital as instantaneous after the emission or absorption of a photon. You don't have to picture it as this definite point of mass having to physically accelerate up or down as in a lift. The old probability wave simply becomes a new probability wave based on the new energy of the electron. The 'in-between' configurations simply don't exist in any meaningful way, not even for the most fleeting instant of time.

#### PeterDonis

Mentor
I'm reading them. I'm just trying to point out to you that you are asking questions that don't have well-defined answers. I suspect you are being misled because you are using ordinary language instead of math. See below.

is there a change of position, albeit indefinite?
What does this even mean? Or, to put it another way, can you rephrase this question using math instead of ordinary language?

When the hydrogen atom is ionised does the does the most probable separation between the proton and electron increase?
When the hydrogen atom is ionized the electron isn't bound at all; it's just the proton left.

I suspect what you meant to ask is, when the hydrogen atom is put in an excited state does the most probable separation between the proton and the electron increase? I think the answer to that, if you are comparing to the ground state, is, AFAIK, always going to be yes, but I'm not positive; I would have to take a look at the actual radial wave functions. Note that, for any state except the ground state, the radial wave functions have multiple peaks, so the idea that there is a single "most probable separation" is no longer really a good way of looking at it anyway.

In any case, you cannot generalize the above to a statement that any excited state with higher energy must have a larger most probable separation than all the states with lower energy.

I agree that the energy of the atom changes but this energy can be equated, in part, to the change of potential energy of the atom
Only if you actually measure it. Otherwise no, you cannot split the energy into a part that's potential energy and a part that's other kinds of energy. You can only say that the atom has some particular energy, corresponding to the stationary state it is in.

All I want to know here is does the mathematical description accommodate measured properties.
Huh? Of course it does.

If so a reference would be useful.
Um, any QM textbook? Have you looked at one?

Quite honestly, this is such a basic part of QM that I am flabbergasted to see this question even being asked. If QM didn't accommodate measured properties, how in the world do you think physicists would have been able to confirm its predictions in experiments?

In certain versions of Millikan's experiment charge is measured by observing charged oil drops which are either at rest or moving with constant velocity in a uniform electric field.
Yes, but those are oil drops, not electrons. An oil drop is a macroscopic object, and the classical approximation works fine for them. In the classical approximation, there is no problem assigning a definite position and velocity to the oil drop.

#### PeterDonis

Mentor
for any state except the ground state, the radial wave functions have multiple peaks, so the idea that there is a single "most probable separation" is no longer really a good way of looking at it anyway.
Also, for any state that is not an s state (i.e., an $l = 0$ state with zero orbital angular momentum), the wave function varies with direction as well as radius, so the concept of a single "most probable separation" doesn't make sense.

I'm reading them. I'm just trying to point out to you that you are asking questions that don't have well-defined answers. I suspect you are being misled because you are using ordinary language instead of math. See below.

What does this even mean? Or, to put it another way, can you rephrase this question using math instead of ordinary language?

When the hydrogen atom is ionized the electron isn't bound at all; it's just the proton left.

I suspect what you meant to ask is, when the hydrogen atom is put in an excited state does the most probable separation between the proton and the electron increase? I think the answer to that, if you are comparing to the ground state, is, AFAIK, always going to be yes, but I'm not positive; I would have to take a look at the actual radial wave functions. Note that, for any state except the ground state, the radial wave functions have multiple peaks, so the idea that there is a single "most probable separation" is no longer really a good way of looking at it anyway.

In any case, you cannot generalize the above to a statement that any excited state with higher energy must have a larger most probable separation than all the states with lower energy.

Only if you actually measure it. Otherwise no, you cannot split the energy into a part that's potential energy and a part that's other kinds of energy. You can only say that the atom has some particular energy, corresponding to the stationary state it is in.

Huh? Of course it does.

Um, any QM textbook? Have you looked at one?

Quite honestly, this is such a basic part of QM that I am flabbergasted to see this question even being asked. If QM didn't accommodate measured properties, how in the world do you think physicists would have been able to confirm its predictions in experiments?

Yes, but those are oil drops, not electrons. An oil drop is a macroscopic object, and the classical approximation works fine for them. In the classical approximation, there is no problem assigning a definite position and velocity to the oil drop.
1. There are certain areas of physics where I like to go back to basic first principles and amongst other things examine the assumptions upon which the maths and theories are based. That's what I'm doing here and I think the questions I'm asking are basically very simple and at this level don't require detailed maths.

2. In a nutshell I wanted to know if the most probable separation between the electron and proton in a hydrogen atom can change. I can express the question in different ways and have done so in this thread. But I can't yet think of a way expressing it mathematically without making it unnecessarily more complicated.

3. b. Yes there are states with multiple peaks but these peaks have different amplitudes as displayed by the radial probability graphs. These indicate that for each orbital there is a single most probable separation. They also show that the higher the energy of the orbital the greater the distance from the nucleus. This seems to confirm what I had suspected all along and what I assumed was obvious and well known. If you find any exceptions to this trend I will be interested to hear of them.

4. It's easy to get the impression that you're being a bit selective about what can be backed up by measurements. For example you seem to accept the concepts of stationary states and there being a structure of radial wave functions with peaks, but you seem to question the concept that there may be a potential energy component of the energy associated with each stationary state.

5. It's possible that you will be less flabbergasted if you consider my question again in the context of what's been discussed in this thread.

The electron is a real thing, it has certain characteristics which include a certain measured mass and a certain measured charge. In some branches of physics these and other characteristics are interpreted as the electron being a particle ... I'm thinking specifically of the standard model.

But, put this assumed particle into another environment such as with a proton such that it becomes part of a hydrogen atom then the electron becomes something else ...... a field quanta ...... an excitation of the electron field. I took the terminology from another thread you participated in. But in the hydrogen atom and other environments the electron is not a particle, or with reference to what you wrote in post 7, it is not a point particle.

So do the measured properties when applied to QFT come up with predictions that accommodate, in other words are compatible with, other theories where the results are interpreted as the electron being a particle.

Looking back I realise that I could have made my point more clearly.

6. I don't think charge measuring methods are relevant to this discussion.

#### vanhees71

Gold Member
Well, you cannot ask a question in theoretical physics, forbid the people you ask to use the adequate language, which is math, and then expect a sensible answer.

The features of "particles" you list as being defined in the standard model is part of the answer: In the standard model you have particle interpretations for asymptotic free states only. To interpret interaction processes as acting forces and accelerating particles as in classical mechanics is at least problematic if not impossible. I tend to think it doesn't make sense since particle interpretations of transient states don't make sense.

In a hydrogen atom of course proton and electron are entangled, but of course you can define sensible quantities to characterize its properties. Among them are statistical quantities like the mean distance between proton and electron, its standard deviation etc.

Well, you cannot ask a question in theoretical physics, forbid the people you ask to use the adequate language, which is math, and then expect a sensible answer.

The features of "particles" you list as being defined in the standard model is part of the answer: In the standard model you have particle interpretations for asymptotic free states only. To interpret interaction processes as acting forces and accelerating particles as in classical mechanics is at least problematic if not impossible. I tend to think it doesn't make sense since particle interpretations of transient states don't make sense.

In a hydrogen atom of course proton and electron are entangled, but of course you can define sensible quantities to characterize its properties. Among them are statistical quantities like the mean distance between proton and electron, its standard deviation etc.
Thank you for your reply which I need to think about. But I would like to respond now to your first comment. The main thing I wanted to find out from this thread is the answer to a question which can be expressed in many different ways using words only. One example is given below:

Is it true that when the hydrogen atom transitions to higher energy level states the most probable separation between the proton and electron increases?

I think the answer is yes and I think it's an answer which is obvious, predictable and widely accepted. But I'm struggling to express the question in terms of mathematics. Any ideas?

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