Cancelation of electron orbital angular momentum

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Discussion Overview

The discussion revolves around the cancellation of orbital angular momentum for two electrons in the same shell and energy state, particularly focusing on the effects of their spins and the implications of Kramer's theorem. The scope includes theoretical considerations of electron configurations and angular momentum in quantum mechanics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions how the orbital angular momentum of two electrons can cancel if they are in the same shell and energy state with opposite spins.
  • Another participant argues that if the electrons are in the same magnetic sublevel state, they should reinforce each other's angular momentum, but notes that electrons typically occupy different sublevel states in practice.
  • A third participant states that "doubly occupied" orbitals have no net angular momentum due to the relationship of the spinors of each pair being related by time reversal, referencing Kramer's theorem.
  • A later reply summarizes the understanding that electrons in doubly occupied orbitals have no net angular momentum and raises several questions about the application of Kramer's theorem, the coupling of spinors, and how this leads to the cancellation of angular momentum.

Areas of Agreement / Disagreement

Participants express differing views on the cancellation of angular momentum in doubly occupied orbitals, with some asserting that it occurs due to time reversal symmetry, while others question the conditions under which this cancellation applies. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

There are uncertainties regarding the application of Kramer's theorem to doubly occupied orbitals, the nature of spinor coupling, and the implications for angular momentum cancellation. These aspects are not fully clarified within the discussion.

bluestar
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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?
 
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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"
 
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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?
 

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