Xjyuk

This is not a duplicate, non of the answers gives a clear answer and most of the answers contradict.

There are so many questions about this and so many answers, but none of them says clearly if the electron's change of orbitals as per QM can be expressed at a time component or is measurable (takes time or not), or is instantaneous, or if it is limited by the speed of light or not, so or even say there is no jump at all.

I have read this question:

Quantum jump of an electron

How do electrons jump orbitals?

where Kyle Oman says:

So the answer to how an electron "jumps" between orbitals is actually the same as how it moves around within a single orbital; it just "does". The difference
is that to change orbitals, some property of the electron (one of the ones described by (n,l,m,s)) has to change. This is always accompanied by emission or absorption of a photon (even a spin flip involves a (very low energy) photon).

and where DarenW says:

A long time before the absorption, which for an atom is a few femtoseconds or so, this mix is 100% of the 2s state, and a few femtoseconds or so after the absorption, it's 100% the 3p state. Between, during the absorption process, it's a mix of many orbitals with wildly changing coefficients.

Does an electron move from one excitation state to another, or jump?

where annav says:

A probability density distribution can be a function of time, depending on the boundary conditions of the problem. There is no "instantaneous" physically, as everything is bounded by the velocity of light. It is the specific example that is missing in your question. If there is time involved in the measurement the probability density may have a time dependence.

and where akhmeteli says:

I would say an electron moves from one state to another over some time period, which is not less than the so called natural line width.

the type of movement in electron jump between levels?

where John Forkosh says:

Note that the the electron is never measured in some intermediate-energy state. It's always measured either low-energy or high-energy, nothing in-between. But the probability of measuring low-or-high slowly and continuously varies from one to the other. So you can't say there's some particular time at which a "jump" occurs. There is no "jump".

How fast does an electron jump between orbitals?

where annav says:

If you look at the spectral lines emitted by transiting electrons from one energy level to another, you will see that the lines have a width . This width in principle should be intrinsic and calculable if all the possible potentials that would influence it can be included in the solution of the quantum mechanical state.
Experimentally the energy width can be transformed to a time interval using the Heisneberg Uncertainty of
ΔEΔt>h/2π
So an order of magnitude for the time taken for the transition can be estimated.

H atom's excited state lasts on average $10^-8$ secs, is there a time gap (of max 2*$10^-8$ secs) betwn. two consec. photon absorpt.-emiss. pairs?

So it is very confusing because some of them are saying it is instantaneous, and there is no jump at all. Some are saying it is calculable. Some say it has to do with probabilities, and the electron is in a mixed state (superposition), but when measured it is in a single stable state. Some say it has to do with the speed of light since no information can travel faster, so electrons cannot change orbitals faster then c.

Now I would like to clarify this.

Question:

1. Do electrons change orbitals as per QM instantaneously?




2. Is this change limited by the speed of light or not?

Do electrons change orbitals as per QM instantaneously?

In every reasonable interpretation of this question, the answer is no. But there are historical and sociological reasons why a lot of people say the answer is yes.

Consider an electron in a hydrogen atom which falls from the $2p$ state to the $1s$ state. The quantum state of the electron over time will be (assuming one can just trace out the environment without issue)
$$|psi(t) rangle = c_1(t) |2p rangle + c_2(t) | 1s rangle.$$
Over time, $c_1(t)$ smoothly decreases from one to zero, while $c_2(t)$ smoothly decreases from zero to one. So everything happens continuously, and there are no jumps.

The reason some people might call this an instantaneous jump goes back to the very origins of quantum mechanics. In these archaic times, ancient physicists thought of the $|2 p rangle$ and $|1 s rangle$ states as classical orbits of different radii, rather than the atomic orbitals we know of today. If you take this naive view, then the electron really has to teleport from one radius to the other.

It should be emphasized that, even though people won't stop passing on this misinformation, this view is completely wrong. It has been known to be wrong since the advent of the Schrodinger equation almost $100$ years ago. The wavefunction $psi(mathbfr, t)$ evolves perfectly continuously in time during this process, and there is no point when one can say a jump has "instantly" occurred.

One reason one might think there is a jump is because, if you have an experimental apparatus that can only answer the question "is the state $|2p rangle$ or $|1s rangle$", then you can obviously only get one or the other. But this doesn't mean that the system has to teleport from one to the other, any more than only saying yes or no to a kid constantly asking "are we there yet?" means your car teleports.

Another, less defensible reason, is that people are just passing it on because it's a well-known example of "quantum spookiness" and a totem of how unintuitive quantum mechanics is. Which it would be, if it were actually true. I think needlessly mysterious explanations like this hurt the public understanding of quantum mechanics more than they help.

Is this change limited by the speed of light or not?

In the context of nonrelativistic quantum mechanics, nothing is limited by the speed of light because the theory doesn't know about relativity. It's easy to take the Schrodinger equation and set up a solution with a particle moving faster than light. However, the results will not actually be trustworthy.

Within nonrelativistic quantum mechanics, there's nothing that prevents $c_1(t)$ from going from one to zero arbitrarily fast. In practice, this will be hard to realize because of the energy-time uncertainty principle: if you would like to force the system to settle into the $|1 s rangle$ state within time $Delta t$, the overall energy has an uncertainty $hbar/Delta t$, which becomes large. I don't think speed-of-light limitations are relevant for common atomic emissions processes.