A Quantum question came with The GRE

[quantumworld]

52) At a given instant of time, a rigid rotator is in the state
psi(theta,phi) = (3/4)^.5 sin(theta)sin(phi), where theta is
the polar angle relative to the z-axis and phi is the azimuthal angle.
Measurement will find which of the following possible values of the z-component of the angular momentum, Lz?
(A) 0
(B) hbar/2, -hbar/2
(C) hbar, -hbar
(D) 2hbar, -2hbar
(E) hbar, 0, -hbar

the answer is C, and I wonder why in vain

Thank you all!

 

[Norman]

try writting the wave function in terms of the eigenstates of the Lz operator. That should make it lucid. And remember that you can only measure eigenvalues of an operator.
Hope this helps.

 

[quantumworld]

thanks Norman for the input,
I did write it in terms of estates, and I got that m = 1, thus evalues should be 1, -1 , 0, but I think I missed something here...

 

[Norman]

I think you mis-wrote it. With a first glance, if I remember correctly, the eigenfunctions of Lz are the Ylm's
$$Y_{lm}$$

And I think that the l=1 term looks something like:

$$Y_{1 m}=(constant)*sin(\theta) e^{i m \phi}$$

writting the sin(phi) term as exponentials, what are the only m terms that show up?