(Solved): For spin-1/2 systems, the spin operators can be written as h(0 1 (0 h(1 07 S. (8) S = 3) S. 2 ...

For spin-1/2 systems, the spin operators can be written as h(0 1 ?(0 h(1 07 S. (8) S? = 3) S. 21 2 i 2 0 -1, Find: (a1) the eigenvalues m, of S. (a2) the normalized eigenvectors X and X of S A spin-1/2 system is in the state y) = (¹+i) 1 Ja 2 b. If spin is measure in the x-direction, what is the probability of finding eigenvalue +h/2? Calculate the expectation values (S.) and (S.) for the given spin state ). Consider next a system of spin-1 system, the spin operators can be written as 0 1 0 0 -i 0 1 0 0 ? ? S. 101 S? i 0-i S. h 0 0 0 ??2 ??2 0 1 0 0 i 0 0 0-1) Find: (d1) the eigenvalues m, (d2) the normalized eigenvectors X of S If the system is in the state m? = ?, calculate (el) (S.) (e2) (S²) (3) (AS.) d. =