Hydrogen Atom States Before Photon Emission | Help

[Shing Ernst]

I have some confusions, and I would like some help:
What states will hydrogen atom be before it emits a photon?
Will it possible be superposition of its eigenstates? (If so, then by measuring the energy of photon, we measure its' energy causing its wavefunction collapse, am I right?)

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edit: Given we have absolutely no knowledge to what has happened to it previously.

 

[PeterDonis]

What states will hydrogen atom be before it emits a photon?

This is way too vague to answer. A hydrogen atom under what conditions?

Will it possible be superposition of its eigenstates?

Eigenstates aren't a property of the atom. They're a property of an observable--i.e., of what measurement we choose to make on the atom.

(If so, then by measuring the energy of photon, we measure its' energy causing its wavefunction collapse, am I right?)

Whether or not the wave function collapses depends on what interpretation of QM you pick. But all interpretations make the same predictions for the results of all experiments, so they're indistinguishable physically. Here at PF we prefer to concentrate on the actual physical predictions.

 

[Shing Ernst]

Thanks for your reply!

This is way too vague to answer. A hydrogen atom under what conditions?

I would like to know the non-relativistic case with the potential is simply -e²/r.

Eigenstates aren't a property of the atom. They're a property of an observable--i.e., of what measurement we choose to make on the atom.

but it sounds strange to me if we measure hydrogen's energy. Surely it doesn't emit a photon when we measure the energy (it has no way of knowing we want to measure it) So I assume it emits "spontaneously" a photon. I wonder what stats it was before emitting a photon. A superposition of energy eigenstates?

Whether or not the wave function collapses depends on what interpretation of QM you pick. But all interpretations make the same predictions for the results of all experiments, so they're indistinguishable physically. Here at PF we prefer to concentrate on the actual physical predictions.

I would love to ... but that's what I can't... (I have a hard time distinguishing a actual prediction from interpretation)
So is it true:
The hydrogen atom emitting a photon and then being measured. (assuming it is in a superposition of energy eigenstates, which I am not sure, and what I would like to know as asked above)
Is this the process how we measure the energy of the hydrogen?

 

[PeterDonis]

I would like to know the non-relativistic case with the potential is simply -e2/r.

Still too vague. Is the atom by itself? What has happened to it previously? Why do you think it will emit a photon?

It looks to me like you would do well to study a basic QM textbook.

 

[Shing Ernst]

Still too vague. Is the atom by itself? What has happened to it previously? Why do you think it will emit a photon?

It looks to me like you would do well to study a basic QM textbook.

The hydrogen atom is in vacuum and well isolated. No one is measuring it (except for some detectors waiting there for photons, which have no interaction with it). However, I think I wrote the potential term already indicated it is isolated. (please point it out otherwise)
I think the confusing part is I did not make it clear:
Whether it was in what excited state or not, we do not know ---- we have absolutely no knowledge of what has happened to it previously. And that's what I would like to know (what exactly states it was before emitting a photons)

Does it sound less vague to you now?

 

[PeterDonis]

The hydrogen atom is in vacuum and well isolated. No one is measuring it (except for some detectors waiting there for photon which have no interaction with it).

Ok, that helps some. But see below.

Whether it is in an excited state, we have absolutely no knowledge of what has happened to it previously.

In other words, we don't know whether or not it is in an excited state? If that's the case, then we don't know whether or not it will emit a photon. And if it is in an excited state, we can't predict when it will emit a photon, or how many it will emit. All we can know is the possible energies (frequencies) of emitted photons that we might observe, based on the energy levels of the atom.

If we know absolutely nothing about the atom's state, then it is also possible that it is in a superposition of energy eigenstates (which I think are the kind of eigenstates you were thinking of in the OP). But that just means we don't know, once again, whether the atom will emit a photon, or when, or how many.

In other words, if we know absolutely nothing about the atom's state, then we know absolutely nothing about the atom's state. And since that appears to be your hypothesis, I'm not sure what else to say.

 

[Shing Ernst]

If we know absolutely nothing about the atom's state, then it is also possible that it is in a superposition of energy eigenstates (which I think are the kind of eigenstates you were thinking of in the OP). But that just means we don't know, once again, whether the atom will emit a photon, or when, or how many.

In other words, if we know absolutely nothing about the atom's state, then we know absolutely nothing about the atom's state. And since that appears to be your hypothesis, I'm not sure what else to say.

Thanks for reply!

Is my understanding correct?
Given the hydrogen atom is in a superposition of energy eigenstates, so it may or may not emit photon(s). but when it does, ( after reading the detector) we can be sure what eigenstate it is after the detection.
And is this whole process what we call measurement? (at least in this case)

Hope you don't mind if I whisper a bit about the Copenhagen interpretation here: it (may or may not) collapses itself, before we "know" it's states, and without interaction (maybe some interaction from the vacuum, but I do not understand it at all)

 

[PeterDonis]

Given the hydrogen atom is in a superposition of energy eigenstates, so it may or may not emit photon(s). but when it does, ( after reading the detector) we can be sure what eigenstate it is after the detection.

Yes. (At least, assuming that the frequency of the detected photon rules out all but one energy level transition, which I believe will be the case for hydrogen.)

is this whole process what we call measurement? (at least in this case)

Technically, detecting the photon only measures the photon; we are deducing the state of the atom after the measurement.

Hope you don't mind if I whisper a bit about the Copenhagen interpretation

Particular interpretations are really not suitable for discussion here, since, as I said before, they are not experimentally distinguishable.

 

[vanhees71]

If the hydrogen atom emits a photon spontaneously the only thing you can say is that it was not in its ground state before. The ground state (and only the ground state) is really stable. In any other state the hydrogen atom sooner or later emits one or more photons. This is called spontaneous emission. To fully understand it, you need quantum-field theory, i.e., the quantization of the electromagnetic field (which is in fact the only way to make sense of what's meant when someone talks about photons to begin with). This is, however, beyond the B level of this thread.

I'd recommend to learn non-relativistic quantum theory first. Take a good textbook and don't worry too much about "interpretation". Just go with the formalism and the minimal interpretation, which is just Born's rule (probabilistic meaning of quantum states). I'd recommend Sakurai, Modern Quantum Mechanics as a starter. Then you can dig deeper. For an excellent treatment of "non-relativistic QED" (i.e., the matter as electrons and protons in the hydrogen atom are treated non-relativistically, which in this case is a very good approximation, while the quantized electromagnetic field is necessarily treated relativistically), see Weinberg, Lectures on Quantum Mechanics. I also recommend the discussion on "interpretation" in this book, because it's well-founded in physics rather than philosophy :-).

 

[Shing Ernst]

...

I'd recommend to learn non-relativistic quantum theory first. Take a good textbook and don't worry too much about "interpretation". Just go with the formalism and the minimal interpretation, which is just Born's rule (probabilistic meaning of quantum states). I'd recommend Sakurai, Modern Quantum Mechanics as a starter. Then you can dig deeper. For an excellent treatment of "non-relativistic QED" (i.e., the matter as electrons and protons in the hydrogen atom are treated non-relativistically, which in this case is a very good approximation, while the quantized electromagnetic field is necessarily treated relativistically), see Weinberg, Lectures on Quantum Mechanics. I also recommend the discussion on "interpretation" in this book, because it's well-founded in physics rather than philosophy :-).

Thank so much for your suggestions! I would like to ask: I have taken one year quantum mechanics last year; however, it did not cover perturbation theory. (also the uncertainty principle still confuses me) Am I prepared well to read Sakurai's modern quantum mechanics?

 

[vanhees71]

I think with the preparation of a one-year introductory QM course, you are good to read Sakurai.