Quantum Mechanics Demystified 2nd Edition David Mcmahon Now

A particle is in the state [ \psi(\theta,\phi) = \sqrt\frac158\pi \sin\theta \cos\theta e^i\phi. ] Find the expectation value ( \langle L_z \rangle ) in units of (\hbar).

In position space, the eigenfunctions are the spherical harmonics ( Y_l^m(\theta,\phi) ). Quantum Mechanics Demystified 2nd Edition David McMahon

We write the eigenstates as (|+\rangle) (spin up) and (|-\rangle) (spin down): A particle is in the state [ \psi(\theta,\phi)