I understand that atomic orbitals are solutions to the time-independent Schrödinger equation, and that they are are analogous to standing waves ("stationary states"). However, even a standing wave has motion, in the sense that (at points other than the nodes) the amplitude varies with time. My question is, do atomic orbitals or spherical harmonics, as standing waves in 3D space, also have such motion? Intuitively, do they "pulse" or "breathe"?
(More precisely, my question is in regard to the behavior of an isosurface of an orbital, the often-pictured shell containing some arbitrary probability, as atomic orbitals themselves have infinite spatial extent.)