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Physics
Quantum Physics
What is the reason behind fermions being unable to share the same quantum state?
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[QUOTE="mikeyork, post: 5620249, member: 22888"] Good question! The L+S rule comes from SU(2) couplings given the usual anti-symmetry. Off the top of my head I think the answer to your question is that you can't get those two specific orbital states in the CM frame because of the spatial symmetry relating the angular co-ordinates (their momenta point in opposite directions). So, for instance you could have l1 = l2 = 1 and then the L=1 state would require s1 = s2. From memory I think the original rule comes from the classic Jacob & Wick* paper on helicity states, but you can also find it in my spin-statistics papers (which I haven't linked because they are not accepted mainstream for other reasons). PM me if you want further information. *M. Jacob and G. Wick, “On the general theory of collisions for particles with spin,” Annals Phys. 7 (1959) 404–428. (I can't locate my copy at this moment but, IIRC, they give the partial wave analysis of identical particle scattering in the CM frame.) Later edit: Also check out Rose "Elementary Theory of Angular Momentum", Chapter XII, section 38 ("Identical Particles in L-S coupling"). [/QUOTE]
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Quantum Physics
What is the reason behind fermions being unable to share the same quantum state?
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