Timeline for The Node Theorem - an argument from physics
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 20, 2023 at 12:38 | comment | added | Qmechanic | Related Phys.SE question: physics.stackexchange.com/q/295857/2451 | |
| Jun 3, 2020 at 3:36 | comment | added | Alexandre Eremenko | @Benjamin, I am not sure about physics but Sturms original proof, as reproduced in Ince, is quite intuitive. | |
| Jun 2, 2020 at 16:41 | comment | added | tzy | @AlexandreEremenko Thanks, those look like some interesting reads! But does anyone have anything to say about the intuitive proof from physics? | |
| Jun 2, 2020 at 14:47 | review | First posts | |||
| Jun 2, 2020 at 14:49 | |||||
| Jun 2, 2020 at 14:39 | comment | added | Alexandre Eremenko | See also the book Gantmakher and Krein, Oscillation matrices, etc. which discusses this in very great detail. | |
| Jun 2, 2020 at 14:38 | comment | added | Alexandre Eremenko | The standard name in mathematics is Sturm's Oscillation Theorems. It is proved in many books and there are several different proofs. For example, Ince, Ordinary Differential equations does not use Prufer's variables. It is close to the original proof of Sturm. | |
| Jun 2, 2020 at 14:33 | comment | added | tzy | Yes, @CarloBeenakker, I actually think so. I think the class of functions will have to be restricted to ones that are somewhat similar to the infinite well or the harmonic oscillator. Maybe a convex potential or something like that - then it looks plausible to handle. Thanks, I will look into that! | |
| Jun 2, 2020 at 12:49 | comment | added | Carlo Beenakker | I think it's called the "oscillation theorem"; it does not hold, for example, for a double-well potential; a weaker version, that the number of zeroes increases with energy without necessarily increasing by one for each subsequent level, holds more generally. | |
| Jun 2, 2020 at 12:34 | history | asked | tzy | CC BY-SA 4.0 |