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# notes26 - 5.73 Lecture #26 26 - 1 HSO + HZeeman in JLSMJ...

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l 5.73 Lecture #26 26 - 1 H SO + H Zeeman in JLSM J and LM L SM S Last time: H SO = ζ l s JLSM J H Zeeman =− γ B z ( L Z + 2 S Z ) → LM L SM S OK to set up H in either basis problem about H Zeeman in Coupled Basis need to work out explicit transformation between basis sets to evaluate matrix elements of H Zeeman in coupled basis. Today: 1. Ladders and Orthogonality method for JLSM J ⟩ ↔  LM L SM S (coupled uncoupled) transformation, term by term. 2. evaluate H Zeeman in coupled basis for 2 P state. 3. Correlation Diagram, Noncrossing Rule * simple patterns without calculations * guidance for “intermediate case” War between two limits 0 * one term creates E () 0 ij 1 * other term causes H 0 ij The two terms play opposite roles in the two basis sets. 4. Stepwise picture of level structure working out from 2 opposite limits * strong spin-orbit, weak Zeeman * strong Zeeman, weak spin-orbit Distortions from limiting patterns (via 2nd-order nondegenerate perturbation theory) give the “other” (pattern distorting) parameter. How does a zero-order picture identify the “picture defining” and the “picture destroying parameters. updated November 4, 2002

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LS =+ 5.73 Lecture #26 26 - 2 H Zeeman =−γ B z ( L z + 2 S z ) =−γ B z ( J z + S z ) OK Not OK for coupled basis to evaluate matrix elements of L z or S z in JLSM J need to work out JLSM J = a m L LM L SM S = M J M L M L ladders and orthogonality J ± = L ± + S ± begin with "extreme" JL S M J = J ; M L = L, M S = S basis states where there is a 11 correspondence : JLSM J = J = LM L = L SM S = S = L + S + + J LS L S = ( L + S ) LL SS 12 + + + + [ ( )( ++ 1 ) ( )( +− 1 ) ] / L S 1 = 12 1 [ L ( L + 1 ) L ( L 1 ) ] / LL SS + [ S ( S + 1 ) S ( S 1 ) ] / LL SS 1 / / L S 1 = [ 2 L ] LL 1 SS + [ 2 S ] LL SS 1 + + / + [ 2 ( ) ] / / L S + + L S 1 = LL 1 SS + LL SS 1 + + for 2 P L = 1, S = 1/2 32 1 1 2 1 2 2 3 10 1 2 1 2 1 3 11 1 2
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## This note was uploaded on 11/28/2011 for the course CHEM 5.74 taught by Professor Robertfield during the Spring '04 term at MIT.

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notes26 - 5.73 Lecture #26 26 - 1 HSO + HZeeman in JLSMJ...

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