Aren’t the spherical harmonics functions with domain S^2, the sphere? I think the solutions to the (time-independent) Schrödinger equation for an electron in a hydrogen atom are given by like, a product of a function of distance from the center with one of the spherical harmonics, or something like that?
It's actually more confusing IMHO, because these graphs overload the radial dimension to show probability as "distance from the origin". You have to multiply that by the radial function to get an actual probability distribution, which kinda/sorta looks like these pictures but not really.
Really the harmonics are best understood as something like "wave height on the surface of a sphere". They tell you how the electrons (or whatever) are going to distribute themselves radially, not where they're going in 3D space.
Also FWIW: the much harder thing to grok here (at least it was for me), and that no one tries to tackle, is why the "l" number corresponds directly to angular momentum. In particular "l==0" doesn't look like there's any rotation going on at all.
aeve890|1 year ago
drdeca|1 year ago
momoschili|1 year ago
ajross|1 year ago
Really the harmonics are best understood as something like "wave height on the surface of a sphere". They tell you how the electrons (or whatever) are going to distribute themselves radially, not where they're going in 3D space.
Also FWIW: the much harder thing to grok here (at least it was for me), and that no one tries to tackle, is why the "l" number corresponds directly to angular momentum. In particular "l==0" doesn't look like there's any rotation going on at all.