Timeline for Electron Self-Energy
Current License: CC BY-SA 4.0
22 events
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| Nov 20, 2022 at 16:05 | comment | added | taa | No, that definitely sounds wrong. But again, the reason I posted the question is because I realized it was wrong. Also, I disagree that there is a problem with the first term, but am open to hearing you argument that it is incorrect. I feel happy with the detailed answer I posted yesterday. Maybe you can tell me if you notice any problems with it. | |
| Nov 20, 2022 at 15:20 | comment | added | Foster Boondoggle | Turns out there's already a related discussion here. physics.stackexchange.com/questions/427565/… | |
| Nov 20, 2022 at 15:16 | comment | added | Foster Boondoggle | I think your first term is wrong as well as the third, but you handwave it away so lets not worry about it. Put words to the content of the third term: "the electron at point $x$ repels the electron at point $y$, and we sum over all $x$ and $y$ weighted by the probability to simultaneously find the electron at both $x$ and $y$". Does this sound correct? I think it sounds fundamentally wrong - the electron is not in two places at once. | |
| Nov 19, 2022 at 19:37 | answer | added | akhmeteli | timeline score: 0 | |
| Nov 19, 2022 at 18:36 | history | edited | Qmechanic♦ |
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| Nov 19, 2022 at 18:11 | comment | added | taa | Well, adding QED certainly isn't going to fix the fact that I am doing the zeroth order calculation incorrectly. And I agree that you can't always treat the square of the wave function as a density of charge - but sometimes you can. The purpose of asking this question is to understand exactly when it is and is not appropriate to make that assumption. | |
| Nov 19, 2022 at 18:04 | answer | added | taa | timeline score: 1 | |
| Nov 15, 2022 at 16:48 | comment | added | Foster Boondoggle | One more point: the title of your post is "electron self energy". My references to QED are by way of saying that this is the name given to the theory that first led to a successful understanding of the electron self-energy. The way you are going about it is not well founded, and I don't know how to help you get there from here, short of pointing you at a semester long course in basic QFT. What you say about QED being a small correction presumes that the zeroth order thing you're computing is actually meaningful. It's not. | |
| Nov 15, 2022 at 16:34 | comment | added | Foster Boondoggle | I can only repeat what I said in my second comment above, which you don't seem to have responded to. The squared wave function is not a density of charge, though you might get away with treating it that way in settings where some other system of interest has lower energy than the bound state energy differences. (e.g., For calculating atomic polarizability or some such. There's a name for this approximation but I don't remember it.) Anyway, your mistake is right there at the beginning, and so everything that follows goes wrong. The wave function squared is not a charge density. | |
| Nov 14, 2022 at 16:27 | comment | added | taa | I'd like someone to correct my methodology, but the correction must itself be correct. If you can successfully argue to me that the QED correction is not small, for example, this might be a constructive way to move forward. | |
| Nov 14, 2022 at 16:26 | comment | added | taa | I don't really understand your comment. In my original post, I demonstrated that my 'semiclassical' approach was flawed. I asked how it might be fixed, noting that QED corrections are too small to explain the discrepancy. You then suggested that the self-energy can be calculated with QED, and I reminded you that the correction is too small. You have not yet responded to this point. Now you are arguing to me that my semiclassical approach is flawed, which merely takes us back to where we started, as that was precisely my original point. | |
| Nov 14, 2022 at 1:03 | comment | added | Foster Boondoggle | Your third term looks like an electrostatic energy for a single electron. Imagine a scattering experiment where you locate the electron very precisely by shooting a gamma ray at it. The initial value of $\psi$ will be highly localized in a small region $\Delta x$ immediately after the scattering, before it spreads out. Would you think in this situation that the electron has suddenly acquired a very large electrostatic energy? That then dissipates (to where?) as the wave function spreads out? The framework you're operating from is just not well founded, per my last comment. | |
| Nov 13, 2022 at 17:26 | comment | added | taa | Corrections from QED are expected to be on the order of the fine-structure constant. I don't see how they could possibly cancel out the third term. | |
| Nov 13, 2022 at 4:38 | comment | added | Foster Boondoggle | The third term just doesn't make sense for what you're trying to calculate. It's treating the electron like it's a smeared out object of density $\left|\psi(x)\right|^2$ which is not what the wave function represents, which is the amplitude to find the entire electron at $x$. There's a whole history of attempts to calculate the electron self-energy both classically and in QM up through the early days of QED. Not hard to find. | |
| Nov 12, 2022 at 2:51 | comment | added | taa | How would you calculate the electric potential in this situation? Are you suggesting it is not well-defined? | |
| Nov 12, 2022 at 2:33 | comment | added | Foster Boondoggle | "If I interpret this charge density just as I would in the context of classical electrostatics, I could easily calculate the electric field arising from it" - isn't this the problem? That's not a good interpretation for the problem you're trying to answer. It might work OK in a setting where some other system is slowly changing, but there's no reason to think it would work when you're asking questions about self-interaction. | |
| Nov 12, 2022 at 1:59 | answer | added | AfterShave | timeline score: 1 | |
| Nov 11, 2022 at 22:01 | history | edited | taa | CC BY-SA 4.0 |
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| Nov 11, 2022 at 21:48 | history | edited | taa | CC BY-SA 4.0 |
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| Nov 11, 2022 at 21:47 | history | edited | taa | CC BY-SA 4.0 |
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| S Nov 11, 2022 at 21:45 | review | First questions | |||
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| S Nov 11, 2022 at 21:45 | history | asked | taa | CC BY-SA 4.0 |