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 S
x:
Then, I can use det(S
x-lambda*I) = 0 to get lambda
2-1 = 0 so lambda is either 1 or -1.
Using that in the eigenvalue equation I get S
x*v = +/- v
Which gets me to
Code:
h (0 1)(a) = +/- (a)
4pi (1 0)(b) (b)
Which is equal to
Code:
h (b) = +/- (a)
4pi (a) (b)
Which in my view is only solvable for a = b = 0. ?