QMIIHelium2011

# QMIIHelium2011 - Physics 4143 Supplementary remarks on...

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Physics 4143: Supplementary remarks on helium atomic structure - angular momentum labels Brian Kennedy, School of Physics, Georgia Institute of Technology, Atlanta, Georgia, 30332-0430 The neutral helium atom has two electrons. The total orbital angular momentum ˆ L = ˆ L 1 + ˆ L 2 and total spin ˆ S = ˆs 1 + ˆs 2 . In each case we are dealing with the addition of two commuting angular momentum operators and the theory of angular momentum addition informs us that the resultant is also an angular momentum operator (i.e. satisﬁes the angular momentum commutation relations). In the case of the total spin angular momentum since s 1 = s 2 = 1/2 we are already familiar with the coupled representation eigenstates, the singlet and triplets ˆ S 2 | s 1 , s 2 , S , M S = S ( S + 1 ) ¯ h 2 | s 1 , s 2 , S , M S , ˆ S z | s 1 , s 2 , S , M S = M S ¯ h | s 1 , s 2 , S , M S . Since | s 1 s 2 | ≤ S s 1 + s 2 we have S = 0, M S = 0 and S = 1, M S = 1, 0, 1, respectively. The eigenstates ( coupled representation

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## This note was uploaded on 01/22/2012 for the course PHYS 4143 taught by Professor Kennedy during the Spring '11 term at Georgia Tech.

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QMIIHelium2011 - Physics 4143 Supplementary remarks on...

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