Timeline for Why do we need the Schrödinger equation if we have a wave equation?
Current License: CC BY-SA 4.0
5 events
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| Apr 27, 2021 at 2:20 | comment | added | Sophie Swett | The Schrödinger equation is a linear equation which, for all positive real numbers $\lambda$, admits a solution which is spatially periodic with period $\lambda$ and which evolves by translation. Those conditions make it "a wave equation" in my mind. The main substantive difference from the standard wave equation is that with the Schrödinger equation, a wave's phase velocity depends on its wavelength, whereas with the standard wave equation, all waves have the same phase velocity. | |
| Apr 26, 2021 at 20:22 | comment | added | Emilio Pisanty | It's a loose term without a precise definition. But the term is in active and widespread use, and that's the only thing that actually matters. | |
| Apr 26, 2021 at 19:12 | comment | added | Steven Sagona | @EmilioPisanty, by what definition exactly is it "a wave" equation? Do you have a definition for what constitutes a wave? | |
| Apr 26, 2021 at 17:00 | comment | added | Emilio Pisanty | The Schrödinger equation is a wave equation. It isn't 'the' wave equation, but those are different things. There are plenty of wave equations that are not 'the' wave equation. (Say, the KdV equation, or the paraxial wave equation for the propagation of light in a graded-index optical fiber (a.k.a. the Schrödinger equation).) The notation is somewhat unfortunate (so perhaps 'the' wave equation should have a better name), but it is what it is. | |
| Apr 26, 2021 at 14:32 | history | answered | Steven Sagona | CC BY-SA 4.0 |