# Cancelation of electron orbital angular momentum

How does the orbital angular momentum of two electrons in the same shell and same energy state cancel each others orbital angular momentum, provided both electrons have opposite spin?

If they're in the same magnetic sublevel state, then they shouldn't cancel each other. They should stand to reinforce each other.

But electrons generally don't fill this way. If they're in a p orbital, and they're the only two electrons, then they generally occupy different magnetic sublevel states. If they're in an s orbital, then their orbital angular momentum is by definition already zero.

"Doubly occupied" orbitals have no net angular momentum, because the two spinors of each pair are related by time reversal. Their angular momenta therefore exactly cancel out. Some textbooks gloss over this fact and just show you that the two spins are anti-parallel, but it's also true for the orbital angular momentum. Check out http://en.wikipedia.org/wiki/Kramer%27s_theorem" [Broken]

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OK, to rehash I have:
Electrons in doubly occupied orbitals have no net angular momentum because the spinors of each electron are related by time reversal and look to Kramer’s Theorem for specifics.

Kramer’s theorem indicates: The energy levels of a system, such as an atom that contains an odd number of spin-½ particles, are at least double degenerate in the absence of an external magnetic field. This degeneracy, known as Kramers degeneracy, is a consequence of time reversal invariance.

Putting this together I think I understand that when a fermion pair occupy an orbital that their spinors are coupled

1. I’m not sure how Kramer’s Theorem applies for a doubly occupied orbital.
2. I’m not sure why the spinors couple?
3. When spinors are coupled how do they cause the cancelation of a "double occupied" orbital angular momentum?
4. Is it because the difference orientation of the particle spin also affects the spinor orientation?