# Prove that spin in arbitary direction is hbar/2

1. Oct 17, 2007

### cks

the question is in the jpeg file.

#### Attached Files:

• ###### spin in arbitrary direction.jpg
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2. Oct 17, 2007

How come you don't just solve the eigenvalues for the matrix that you have denoted by $$S_{z'}$$? We are not interested in the eigenvalues of $$S_{z'}^2$$, but just on the eigenvalues of the spin matrix you have constructed in the fourth line of your attachment. I think you have got a bit messed up with the eigenvalues related to the total spin angular momentum $$S^2=S_x^2+S_y^2+S_z^2$$ and the component of spin angular momentum related to an arbitrary direction.