- #1

TheBaker

- 19

- 0

## Homework Statement

The angular part of a system’s wavefunction is

[tex]<\theta, \phi | \psi>\propto (\sqrt{2}\cos\theta + \sin{\theta}e^{−i\psi} - \sin{\theta}e^{i\psi} ). [/tex]

What are the possible results of measurement of (a) [tex]L^2[/tex] , and (b) [tex]L_z[/tex] , and their probabilities? What is the expectation value of [tex]L_z[/tex]?

## Homework Equations

[tex]L^2|E> = l(l+1)|E>[/tex]

## The Attempt at a Solution

I can see that the wavefunction takes the form of the spherical harmonics for l = 1, and from that I think I can say that [tex]L^2[/tex] = 2. However, I'm unsure whether this is correct, or how to find the probabilities.

I haven't had much luck at all with [tex]L_z[/tex].