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Lecture30

# Lecture30 - PHYS 360 Quantum Mechanics Fri Apr 1 2011...

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4/1/11 1 1 PHYS 360 Quantum Mechanics Fri Apr 1, 2011 Lecture 30: If a spin points in the z direcEon, what do you get in the x direcEon? HW #8 due Monday: Ch 4, #24, 26, 27, 28 Last year’s final exam is posted. 2 We assume that spin angular momentum follows all of the rules that we found for the algebraic (operator) theory of angular momentum: L x , L y = i L z ; [ L y , L z ] = i L x ; [L z , L x ] = i L y L 2 , L x = 0, L 2 , L y = 0 , L 2 , L z = 0 L 2 f l m = 2 l l + 1 ( ) f l m ; L z f l m ; = mf l m l = 0, 1/ 2, 1, 3/ 2,...; m = l , l + 1,... , l 1, l Note: the eigenfuncEons are actual funcEons of the coordinates (xyz) or (rθ ϕ ). 3 S x , S y = i S z , S y , S z = i S x , S z , S x = i S y S 2 s m = s s + 1 ( ) 2 s m ; S z s m = m s m S ± sm = s s + 1 ( ) m m ± 1 ( ) s m ± 1 ( ) s = 0, 1 2 ,1, 3 2 ,...; m = s , s + 1,..., s 1, s Note: the eigenfuncEons are NOT funcEons of the coordinates (xyz) or (rθ ϕ )! 4 4.4.1 Spin ½ The electron has spin one-­૒half, and is the most important example. There are only two eigenstates: sm = 1 2 1 2 = sm = 1 2 ( 1 2 ) =

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Lecture30 - PHYS 360 Quantum Mechanics Fri Apr 1 2011...

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