Intuitively: if r and v point in the same or opposite direction, L is zero. So only movement in the direction perpendicular to r contributes to L. Those are the angles.hokhani said:TL;DR: Why in quantum mechanics the angular momentum is independent of the ##r##?
Angular momentum as generator of rotation in defined by ##L=r\times p##. However, none of the angular momentum wave functions depends on the ##r##. They only depend on the angles.
On the contrary, I think the particular case ##l=0## is more understandable from classical view. It describes the particle at rest. However, the quantum particle is not localized at a particular point. We can find it everywhere with the same probability.haushofer said:Intuitively: if r and v point in the same or opposite direction, L is zero. So only movement in the direction perpendicular to r contributes to L. Those are the angles.
By the way, this is also what makes the l=0 states of e.g. hydrogen clasically difficult to understand: it involves movement of a charge along a line through the nucleus. QMically, it means a spherically symmetric wavefunction. Bye bye classical orbits :P
No, the particle can't be at rest because it has nonzero kinetic energy. There is no classical state that corresponds to the ##l = 0## quantum state.hokhani said:I think the particular case ##l=0## is more understandable from classical view. It describes the particle at rest.
This is not correct; the ##l = 0## wave function does not have an equal amplitude everywhere.hokhani said:The quantum particle is not localized at a particular point. We can find it everywhere with the same probability.