Eigenvalue of pauli spin matrices

[moonray]

1. Homework Statement [/
from the ets general physics practice test (ill take it in april) the state of spin 1/2 particles
using the eigenstates up and down Sz up= 1/2 hbar Sz down= -1/2 hbar

Homework Equations

given sigmax (pauli spin matrix) which of the following list of eigenstates has a has an eigenvalue of -1/2 hbar

The Attempt at a Solution

a) down spin
b)1/sqrt2 spin up + spin down
c) 1/sqrt2 spin up -spin down
d) 1/sqrt2 spin up - i (spin down)


I think c is the answer but i can't remember how to put it together could you explain?

 

[nickjer]

Just operate the sigma_x matrix on those vectors and see which one is an eigenvector with a -1/2 hbar eigenstate. Just plug-and-chug as my teachers use to say.