Well, the magnitude of the vectors seems to be 1. After all, |(1 0)|2
is 1. So that would be okay?
For the second question I used the Pauli-spinmatrix of Sx
Then, I can use det(Sx
-lambda*I) = 0 to get lambda2
-1 = 0 so lambda is either 1 or -1.
Using that in the eigenvalue equation I get Sx
*v = +/- v
Which gets me to
h (0 1)(a) = +/- (a)
4pi (1 0)(b) (b)
Which is equal to
h (b) = +/- (a)
4pi (a) (b)
Which in my view is only solvable for a = b = 0. ?