A beam of spin-1/2 particles is prepared in the state
￼￼￼￼a) What are the possible results of a measurement of the spin component Sz, and with what probabilities would they occur?
b) What are the possible results of a measurement of the spin component Sx, and with what probabilities would they occur?
[tex]P_x=\left|\left\langle x\right| \left. \psi \right\rangle\right|^2[/tex]
The Attempt at a Solution
So I can find out the answer to part b just by plugging it straight into the formula and using that [itex]_x\left\langle +\right| \left. + \right\rangle_x=1[/itex] and [itex]_x\left\langle +\right| \left. - \right\rangle_x=0[/itex]
my problem is with the first part of the question. If I use the same method as before I end up with
[tex]_z\left\langle +\right| \left. + \right\rangle_x\\
_z\left\langle +\right| \left. - \right\rangle_x\\
_z\left\langle -\right| \left. + \right\rangle_x\\
_z\left\langle -\right| \left. - \right\rangle_x[/tex] in my equations. And I do not understand how to know what these are.