(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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]?

2. Relevant equations

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

3. 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].

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# Quantum Mechanics - Spherical Harmonics

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