Timeline for Dispersive equations at low frequencies and time oscillations
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 29, 2023 at 20:43 | comment | added | Jules Lamers | It means that the energy is purely kinetic (no potential energy): if the particle (excitation; or wave front, perhaps) doesn't move, it has zero energy | |
| Nov 29, 2023 at 20:16 | comment | added | kieransquared | That helps! Although I'm still wondering why the other equations have $\omega(0)=0$, or what the physical interpretation is there. I'd imagine it's context-dependent. | |
| Nov 29, 2023 at 18:04 | comment | added | Jules Lamers | Physically, the $+1$ for the KG dispersion describes a relativistic particle with some (generally nonzero) mass. Reinserting all physical constants, it reads $E^2 = (m \, c^2)^2 + (c\,p)^2$ with $E$ the energy (your $\omega$), $m$ the rest mass, $c$ the speed of light, and $p$ (your $\xi$) the momentum. The first term on the RHS (your $+1$) is the particle's rest energy, cf Einstein's famous $E=m\,c^2$. For massless particles $m = 0$, and one is left with $E = |\xi|$ like in your other examples. See en.wikipedia.org/wiki/Klein%E2%80%93Gordon_equation for more. Does that help? | |
| S Nov 29, 2023 at 17:55 | review | First questions | |||
| Nov 29, 2023 at 18:06 | |||||
| S Nov 29, 2023 at 17:55 | history | asked | kieransquared | CC BY-SA 4.0 |