TotalOrbitalAngularMomentum

TotalOrbitalAngularMomentum - Total Orbital Angular...

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Colby College Total Orbital Angular Momentum C: 2p 2 or ↑↓ Clebsch-Gordan Series: L = l 1 + l 2 , l 1 + l 2 – 1, …, | l 1 l 2 | L = |M L | max 2p 2 : 1 + 1, …, |1 – 1| = 2, 1, 0 L 0 1 2 3 4 5 2p 2 : D, P, S Term S P D F G H M L = Σ m l M L = Σ m l +1 0 -1 ↑↓ 2 +1 0 -1 1 1 0 0 ↑↓ 0 -1 -1 3 P ↑↓ -2 1 D + 1 S Singlets: L = |M L | max = 2 for a 1 D with M L = 2,1,0,-1,-2, leaving M L = 0 to give a 1 S term. Triplets: L = |M L | max = 1 for a 3 P with M L = 1,0,-1. These diagrams don’t take into account electron indistinguishability. Schematically for example: ↑↓ 1 2 ( ) ↑↓ ↓↑ and all electrons take their turns in p x , p y , and p z . In addition, all degenerate configurations mix as linear combinations (e.g. all the M L = 0 configurations) . configuration: d 1 p 1 for which l 1 = 2 and
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