- #1
Robben
- 166
- 2
Homework Statement
Determine the eigenstates of ##\hat{\mathbb{S}}_x## for a spin##-1## particle in terms of the eigenstates ##|1,1\rangle, \ |1,0\rangle,## and ##|1,-1\rangle## of ##\hat{\mathbb{S}}_z.##
Homework Equations
The Attempt at a Solution
Not sure exactly how to set this problem correctly.
We have for the matrix representation: ##
S_z= \hbar\left[\begin{array}{ c c }1&0& 0 \\0 & 0 &0\\0&0&-1\end{array} \right]## and ##S_x= \frac{\hbar}{\sqrt{2}}\left[\begin{array}{ c c }0&1& 0 \\1 & 0 &1\\0&1&0\end{array} \right].## From this it asks to determine the eigenstates of ##S_x## so do I just find the eigenvalues for ##S_x## and then determine the eigenstates from those? Not sure exactly what is being asked.