Solutions to Problem 3.4
Problem 3.4 is absolutely an exercise in solving the eigenvalue problem. Specifically, we'll solve it for a linear combination of two spin operators, corresponding to rotating the Stern-Gerlach device by an angle in the x-y plane.
The problems can be found here (scroll to the bottom).
https://pasayten.org/quantum-mechanic...
The course itself has a website here:
https://pasayten.org/quantum-mechanic...