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PS+1-solution

# PS+1-solution - Problem Set#1 1 If you measure Sy what are...

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Problem Set #1 1. If you measure Sy, what are the eigenvalues and eigenvectors for a spin ½ particle? S y 2 0 i i0 ; 2 0 i  2 2 i i 2 0 2 i i 2 0  2 So the eigenvalues are Ñ 2 and - Ñ 2 If  2 2 0 i 2 Const. i 1 If  2 2 0 i  2 Const. i 1 After normalization, the eigenvector for Ñ 2 is 2 2 - i 1 , the eigenvector for - Ñ 2 is 2 2 + i 1 2. If a particle starts in state c +, what are the probabilities of obtaining + ћ /2 and ћ /2 if you measure Sy?

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y 2 2 i 1 ; y 2 2 i 1 ; 0 1 ; P 2  y 2 P 2 2 2 ,1 . 0 1 2 P 2 1 2 P 2 y 2 P

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PS+1-solution - Problem Set#1 1 If you measure Sy what are...

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