What does it mean physically for an electron to have zero angular momentum? What keeps it from impinging on the nucleus without the barrier?
An electron by itself always has intrinsic spin angular momentum. But an electron with has zero orbital angular momentum relative to an atomic nucleus. Its wavefunction is spherically symmetric, and in fact, an electron does have some reasonable probability to be near the nucleus (unlike electrons with higher values, which don’t like to be near ). However, because the wavefunction extends well beyond the nucleus, it won’t always be near the origin. It doesn’t need a “centrifugal barrier” to keep it away most of the time; it stays away just from the extended nature of the wavefunction solution to the Schrödinger equation.
