# How quickly do electrons jump orbitals?

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I would like to know how long it takes for an electron to travel from one orbital to another. I suspect there are a bunch of factors that make this question difficult or impossible to answer, but I thought I'd try to see if someone can help.
I would hope something like this would come in handy: ΔEΔt>h/2π. Mainly because it seems relatively simple, although I'm not really sure what the inequality really means, other than there is a certain uncertainty associated with that pair.

But there are some things that really muddy the waters. Like what distance does the electron move when it goes from it's starting point to the new orbital? Presumably that isn't even something that can be answered precisely, because position and momentum are also related by a minimum uncertainty.

Intuitively, I feel like it must be slower than the speed of light, since electrons have mass. But with quantum mechanics, I don't really trust my intuition at all. I mean, is an electron even a localized particle in the first place?

If anyone has insight into the actual speed that an electron moves from one orbital to another, please let me know (including if the concept itself is dated and doesn't really have as much meaning as I think it might).

Thanks!

Delta2

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I would like to know how long it takes for an electron to travel from one orbital to another.
There is no answer to this question; the electron is not a classical object traveling on a specific trajectory from one orbital to another, and there is no well-defined time associated with the change.

aperakh, Twigg, hutchphd and 2 others
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There is no answer to this question; the electron is not a classical object traveling on a specific trajectory from one orbital to another, and there is no well-defined time associated with the change.
This is kind of what I figured, but I was hoping something in QED would have an answer, since it’s a quantum field relativistic theory. But really I was just grasping at fantasy, since I barely know what a field is, let alone QED.

But does it gave anything to do with the energy-time uncertainty relation? I ask because you said there was no well defined time for such a thing (let alone a well defined location for the electron).

Delta2
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does it gave anything to do with the energy-time uncertainty relation?
No.

Keith_McClary
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The arxiv preprint of the actual paper is here:

https://arxiv.org/abs/1803.00545

Note that none of the times being measured in this (very interesting) experiment correspond to "the time it takes for the electron to travel from one orbital to another". Also note that in this experiment, the quantum system is being measured many, many times, so the scenario is very different from an ordinary transition between energy levels in an atom, where the only measurement made is of the spectral line (the frequency of the photon emitted or absorbed).

I would like to know how long it takes for an electron to travel from one orbital to another.
As @PeterDonis said, the question doesn't make sense. However, there are related questions one can ask that do make sense. For example, if an electron makes a transition from one state to another, what is the average amount of time it spend in the first state, before it can be found in the second state. You can see discussion of the lifetimes of various electrons states in
https://chem.libretexts.org/Bookshe...minescence/3.2:_Energy_States_and_Transitions
https://www.nist.gov/pml/atomic-spe...-data-and-formulas/atomic-spectroscopy-atomic

Grasshopper
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How can something happen that it doesn't have a well defined time? Either it is instantaneous or it takes some time.
How does it make sense to ask how much time it spends on one state but it doesn't make sense to ask how much time it takes to switch states?

Seems to me like another absurdity in the theory of quantum physics. The most absurd theory that makes the most accurate predictions loool...

weirdoguy, atyy and PeroK
Jarek 31
There is entire new field measuring this kind of delays since ~2010: attosecond chronoscopy.
~1000 articles citing 2010 Science "Delay in photoemission" (~21 attoseconds): https://scholar.google.pl/scholar?cites=15193546925951882986&as_sdt=2005&sciodt=0,5&hl=en

E.g. 2020 "Probing molecular environment through photoemission delays" https://www.nature.com/articles/s41567-020-0887-8
Attosecond chronoscopy has revealed small but measurable delays in photoionization, characterized by the ejection of an electron on absorption of a single photon. Ionization-delay measurements in atomic targets provide a wealth of information about the timing of the photoelectric effect, resonances, electron correlations and transport.

Keith_McClary, vanhees71, atyy and 1 other person
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The energy-time uncertainty relation and the question of the kind posed here is among the more diffcult questions about quantum theory. For sure there are no jumps, and the "transition time" from one state to another is also not a well-defined concept but determined pretty much by what's really measured.

The most simple standard treatment for the emission of a photon due to the transition of an atom from an excited state to a lower energy eigenstate is 1st-order time-dependent perturbation theory. Here you have an energy-time uncertainty relation between the "natural linewidth" and the "formation time" of the photon.

For the inverse process, the photoelectric effect, which is a transition from an atomic bound state to the continuum states by absorption of a photon, you find the calculation in my Insights article

https://www.physicsforums.com/insights/sins-physics-didactics/

Grasshopper
Photoemission is kind of the opposite process. You try to ionize some atom or molecule and check how long it takes until the electron gets ejected.

As for the initial question: it depends. Consider, e.g., an electron going from a higher energy state to a lower energy state. It needs to get rid of the excess energy. The typical way to do so would be by emitting a photon. This process is well understood. Actually, it turns out that usually the atom is usually perturbed first and goes into a superposition state between the initial and the final state, which is coupled to the light field. Loosely speaking, you get oscillations in the probability of where to find the difference energy between the excited state and the ground state.

Initially, if you checked where the energy is, you would find the atom in the excited state and the light field empty. After some time, you would find the atom in the ground state and the light field containing a photon. Even later, you would again find the atom in the excited state and the light field empty. Even later, you would find a photon in the light field and the atom in the ground state and so on and so forth.

Of course there is a caveat: The probability amplitudes for finding the energy in the atom and in the light field oscillate, but just like for any superposition state, you cannot just go and check what the state of the superposition is. Any kind of measurement - including deliberate measurements and interactions with the environment - will break the superposition, so you will find the energy either in the atom or in the light field. Accordingly, my response to the question "How long does it take for the electron to go from state A to state B" would be: There are two timescales. The time of the total transition is given by how well the system is separated from its environment and how long it takes (on average) for an interaction to occur - this would be extremely short for the case of photoemission mentioned above. The other timescale is the frequency of the probability amplitude oscillation. The first quantity corresponds to the coherence time of the emitted light. The second quantity is related to the dipole moment of the transition.

Grasshopper, Jarek 31 and vanhees71
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How can something happen that it doesn't have a well defined time?
This is QM. Lots of things aren't well defined that your intuition might think should be.

How does it make sense to ask how much time it spends on one state but it doesn't make sense to ask how much time it takes to switch states?
It doesn't make sense to ask how much time it spends in one state either. You can't continuously track a quantum object; it doesn't have a continuous trajectory. That's not what any of the experiments being referred to are doing.

Staff Emeritus
How can something happen that it doesn't have a well defined time? Either it is instantaneous or it takes some time.
How long does it take someone to lose all their money in a casino?

This question, like many in QM, is not well defined. To be well-defined, the statement needs to resolve around measurements. For example, a system is prepared in state X. At t1, it is measured to be in state A. At t2, it is measured to be in state B. One could plot the probability that B is different from A as a function of t2 - t1. That is at least well-defined.

Twigg, Grasshopper and vanhees71
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How can something happen that it doesn't have a well defined time?
Niels Bohr would have argued that by a well-defined time you must mean the difference between two readings on a clock (being the appropriate macroscopic measuring device). However, if all you have is an emitted photon, then there is nothing about that photon that tells you how long the atom took to produce it!

You cannot see the electron in one orbital and then see it in the second. The act of measuring the electron in the first case would destroy the initial state - and the quantum jump you are waiting for would simply never happen. In other words, direct, continuous measurements of atomic phenomena are simply not possible.

This is central to the original Bohr/Heisenberg argument that atomic theory must focus on what can be measured - and, in this case, what can be measured is the wavelength of the emitted photon.

Grasshopper
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Niels Bohr would have argued that by a well-defined time you must mean the difference between two readings on a clock (being the appropriate macroscopic measuring device). However, if all you have is an emitted photon, then there is nothing about that photon that tells you how long the atom took to produce it!

You cannot see the electron in one orbital and then see it in the second. The act of measuring the electron in the first case would destroy the initial state - and the quantum jump you are waiting for would simply never happen. In other words, direct, continuous measurements of atomic phenomena are simply not possible.

This is central to the original Bohr/Heisenberg argument that atomic theory must focus on what can be measured - and, in this case, what can be measured is the wavelength of the emitted photon.
Let me see if I understand this.

In order to know how long something takes, you need TWO readings of time (obvious of course). But all we have are photon emissions to go by, which means we'd only have one time. We could presumably find an average rate of electrons changing energy levels, but definitely not how fast that takes for a single electron, since we'd only have the ending time (and this isn't even getting into the notion that we can't assign a defined location to an electron until we measure it in the first place).

But, if that's correct, can we at least not figure out some sort of boundaries on how long that must take, if not an exact time interval?

I ask because I found this interesting article arguing that wave function collapse may take a finite amount of time:

https://iopscience.iop.org/article/10.1088/1742-6596/410/1/012153/pdf

(Journal of Physics)

If it turns out that that has a finite time limit, could this as well? And if it's not the speed of light, I'd nominate the speed of wave function collapse as a candidate.

I base that on nothing other than it would look pretty. And the fact that it clearly can't take an infinite amount of time, since the universe has not been around for eternity.

Staff Emeritus
I found this interesting article

Pure crackpottery.

You will not learn QM by reading random articles by random crackpots.

vanhees71
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Pure crackpottery.

You will not learn QM by reading random articles by random crackpots.
I mean I figured Journal of Physics (even "Conference Series") was trustworthy. ("A Yu Ignatiev 2013 J. Phys.: Conf. Ser.410 012153")

But perhaps I read the "to cite article” data incorrectly. Then again, when I looked up IOP Publishing before posting it (https://en.wikipedia.org/wiki/IOP_Publishing) it is claimed to be the publisher of Institute of Physics (https://en.wikipedia.org/wiki/Institute_of_Physics), so I assumed it was trustworthy.

But again, perhaps not. After all, anyone can name themselves something that sounds reputable.

EDIT - Let me add that if I posted an article that isn’t from a reputable source, it was by mistake. Crackpots give me AIDS. I have a deep loathing of them, which is which is why I googled the site, which is how I found the publisher is associated with Institute of Physics, which is why I assumed the source was reputable

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It is Journal of Physics: Conference Series .
Peer review is done by the conference organizers.
I think conference presentations can sometimes be more speculative than what is allowed in regular journals.
So, just to be clear, you're saying that what is allowed in Journal of Phyiscs: Conference Series is in fact crackpottery?

I mean, I'm not at the level anyway. I know what some of the mathematical symbols mean as they are used in vector calculus. I'm certainly not trying to learn physics from crackpottery that is allowed in Journal of Physics: Conference Series.

But surely crackpottery wouldn't be allowed, and if so, I feel like Institute of Physics/Journal of Physics need to be chastised by the physics community for leading the general public and students astray, as well as for soiling their names.

EDIT - The tone here is not meant to be biting or sarcastic. I'm deadly serious. How can something that is crackpottery be allowed to be published on ANYTHING that has the name of a peer reviewed journal on it? Speculation, I'd understand. Cutting edge stuff that still needs to go through the peer review process, yeah. But crackpottery? That's not excusable to me.

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I found this interesting article arguing that wave function collapse may take a finite amount of time:

vanhees71
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In order to know how long something takes, you need TWO readings of time (obvious of course).
No. In order to know how long something takes, you need to be able to continuously track it through time. This is not possible in QM. It is only possible in classical physics, and only to the extent that you can interact with a system in classical physics without changing its dynamics (which is to say, only as a limiting case which can never be exactly realized in practice, even in classical physics).

If all you have is two "snapshots" of something, you don't know what it was doing in between. Say snapshot #1 shows the thing in state A and snapshot #2 shows the thing in state B. That does not mean you can subtract the times of the two snapshots and know how long it took to go from state A to state B. It could have taken only part of the time. Nor can you say that whatever happened would have taken the same time had you not taken the snapshots at all. Taking snapshots is an interaction, and changes the system you are interacting with.

aaroman and Grasshopper
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@PeterDonis for QM you recommend Ballentine's book, which book do you recommend for QFT?

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which book do you recommend for QFT?
I don't have a single book on QFT I would recommend. The only thing I can recommend is to try as many of the "standard" texts in the field as you can.

Delta2
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I am not sure but I think its still an open problem of whether we can assign a wave function to a single photon. Some researchers say we can, some say we cannot. Maybe the majority says that we cannot.

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I think its still an open problem of whether we can assign a wave function to a single photon.
It depends on what you mean by "wave function". However, it is not an open question whether there is a well-defined position operator for a photon (which is the claim @Jarek 31 is making); there isn't.

vanhees71 and Delta2
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It depends on what you mean by "wave function". However, it is not an open question whether there is a well-defined position operator for a photon (which is the claim @Jarek 31 is making); there isn't.
I mean the usual wave function. The electron as a particle has a wave function, the photon which also is a particle (not in the usual sense though) must have a wave function as well shouldn't it?

weirdoguy
I mean the usual wave function.

"Usual" wave function is part of formalism of non-relativistic QM. Photons are ultra-relativistic so "usual" formalism does not apply. The thing is how to generalise it.

Delta2
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I mean the usual wave function. The electron as a particle has a wave function, the photon which also is a particle (not in the usual sense though) must have a wave function as well shouldn't it?
The electron has a rest frame and the photon doesn't. You should be familiar with false syllogisms:

First premise: The electron is a particle.
Second premise: The electron has property X.

False conclusion: all particles have property X.

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Yes, well in introductory (and non relativistic) QM texts you read quite often "The wave function of a particle is ..." or "The wave function of a particle has this property..." so you easily can form the false impression that all the particles can have wave function.

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Yes, well in introductory (and non relativistic) QM texts you read quite often "The wave function of a particle is ..." or "The wave function of a particle has this property..." so you easily can form the false impression that all the particles can have wave function.
Good old Griffiths leaves the reader in no doubt:

The photon ... is a relativistic object if ever there was one, and therefore outside the scope of non-relativistic QM. It will be useful in a few places to speak of photons ... but please bear in mind that this is external to the theory we are developing.

Delta2
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I mean the usual wave function. The electron as a particle has a wave function, the photon which also is a particle (not in the usual sense though) must have a wave function as well shouldn't it?
The electron as a particle has a wave function in the non-relativistic limit. What really makes relativistic QT different from non-relativistic QT is that in interactions of "particles" there's always the possibility to create new particles and/or destroy particles. That's why a single-particle wave function for an interacting particle can at best be an approximation. What you need is some description that allows to take the creation and destruction of particles into account, and the most convenient way is quantum field theory. That's why relativistic QT nowadays is formulated as local relativistic QFTs.

Massless "particles" are special in the sense that they have no non-relativistic limit, and that's because there's no "mass gap" to overcome to create them. E.g., even at the lowest collision energies of charged particles or of photons with charged particles there's always the possibility to create "soft photons" ("Bremsstrahlung").

Also formally massless particles do not make sense in non-relativistic quantum mechanics, because the representations of the quantum version of the Galileo group with ##m=0## don't lead to a physically sensibly interpretable dynamics.

Last but not least, for the photon as a massless particle with spin ##1>1/2## you cannot define a position observable in the usual sense. So it is already impossible to formulate a single-photon wave function to begin with.

Delta2 and PeroK
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Hopefully not full on crackpottery though, because yeah I’d be pretty upset and disappointed in the brands involved (which are supposedly reputable).

Anyway, it appears that the question in the context of established quantum mechanics is like asking what the color of middle C is (e.g., entirely meaningless). It is unfortunate there is a disconnect of this nature between QM and classical physics, but it’s not like I’m in position to understand a potential breakthrough on that front anyway.

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The electron as a particle has a wave function
In non-relativistic QM, yes.

, the photon which also is a particle (not in the usual sense though) must have a wave function as well shouldn't it?
No, because there is no non-relativistic model of a photon; they are inherently relativistic.

vanhees71
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Is photon the only particle of the standard model that doesn't have a wave function or there are others too, for example an electron having relativistic speed doesn't have a wave function either?