Chapter4_19 - PHY4604 R. D. Field Department of Physics...

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Unformatted text preview: PHY4604 R. D. Field Department of Physics Chapter4_19.doc University of Florida Spin Angular Momentum Spin Angular Momentum: If we define r h r 2 1 = S where z y x z y x + + = r then op k ijk op j op i S i S S ) ( ] ) ( , ) [( 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 = ! 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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