The spin operator in an arbitrary direction can be written as

(0,0) = sin cos o + y sin sin + ₂ cos 0,

I

where the Pauli spin matrices are given by

0

(13),

1. Find the eigenvectors and eigenvalues for the operator ô(0, 6).

ÔT

x

=

Oy

=

0

(² i).

i

0

Oz

=

0

0 -1