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

```
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. ?