Timeline for Why do sums become integrals in quantum mechanics of infinite basis states?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 20, 2023 at 17:28 | vote | accept | TunaSandwich | ||
| Apr 19, 2023 at 21:06 | comment | added | E. Anikin | Thank you! I'll take a look at Villani. | |
| Apr 19, 2023 at 21:03 | comment | added | FlatterMann | I agree, the problems with continuous spectra of linear operators are extremely subtle. Like I said, they also don't matter much in physics. Your answer is, IMHO, perfectly fine for most physicists most of the time. It gets the job done. I just wanted to point out that the proper mathematical techniques that were developed in functional analysis are very different from the physics approach. They are also vastly more powerful. If you want to see a beautiful hard-core application of functional analysis to a physics problem, look at Cedric Villani's work on Landau damping. | |
| Apr 19, 2023 at 20:58 | comment | added | E. Anikin | Although I agree that this argumentation is handwaving, I don't see how the question you cited shows that it doesn't work. The question is about some normalization issue which is resolved in the answer to the question. In my answer, normalization is also taken into account accurately. I think the caveats are more subtle (and I'd like to learn them some day) | |
| Apr 19, 2023 at 20:34 | comment | added | FlatterMann | Yes, that's the usual physical handwaving. This post math.stackexchange.com/questions/4086667/… shows why it doesn't really work. To a physicist it doesn't matter most of the time that it doesn't work, to a mathematician it does. The proper mathematical theory to do this "correctly" has been around for eighty plus years now, I believe. That physicists are not using it much (if at all) is practical: it doesn't actually address the real problems with continuous states that pop up in QFT where they matter. | |
| Apr 19, 2023 at 19:41 | history | answered | E. Anikin | CC BY-SA 4.0 |