Find the probability of measuring spin up an axis.

[Calu]

Homework Statement

Set |Ψ> = (1/√ 2) | ↑, z> + (e^iθ / √ 2) | ↓, z>.

Find the probability of measuring the spin component of s_z to be up the z-axis.
Find the probability of measuring the spin component of s_x to be up the x axis.

Homework Equations

I'm not sure.

The Attempt at a Solution

I think I have to find the projection along each axis in the required direction and then multiply by the complex conjugate. How would I go about finding a projection?

Also, I have an equation for <s_z>. Is this the same as finding the probability of spin up the z-axis?

 

[Telemachus]

What gives you the probability of finding the particle in a determinate state in quantum mechanics?