Chapter7_11 - PHY3063 R. D. Field Department of Physics...

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Unformatted text preview: PHY3063 R. D. Field Department of Physics Chapter7_11.doc University of Florida Spin ½ Angular Momentum Spin ½ Angular Momentum: If we define σ r h r 2 1 = S where z y x z y x ˆ ˆ ˆ σ σ σ σ + + = r then op k ijk op j op i S i S S ) ( ] ) ( , ) [( ε h = and ] ) ( , [ 2 = op i op S S where = + + = 1 1 2 4 3 2 2 2 2 h z y x op S S S S and > + >= = = >= v s s v v v v v v S op | ) 1 ( | 1 1 | 2 2 4 3 2 1 2 4 3 2 1 2 4 3 2 h h h h The two component spinors are eigenkets of (S 2 ) op with eigenvalue s = ½ ! Eigenkets of (S z ) op : We must sove the eigenvalue equation > >= v m v S op z | | ) ( h = − = − 2 1 2 1 2 1 2 1 2 1 1 1 v v m v v v v h h h or ) ( ) ( 2 2 1 1 2 1 = + − − v m v m The eigenvalues are...
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This note was uploaded on 05/29/2011 for the course PHY 3063 taught by Professor Field during the Spring '07 term at University of Florida.

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