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

A particle is in the state [itex]\psi = R(r)(\sqrt{\frac{1}{3}}Y_{11} + i\sqrt{\frac{2}{3}}Y_{10})[/itex]]. If a measurement of the x component of angular momentum is made, what are the possible outcomes and what are the probabilites of each?

2. Relevant equations

[tex]L_{\pm}Y_{lm}=\sqrt{l(l+1)-m(m \pm 1)}Y_{l(m\pm 1)}[/tex]

[tex]L_x = \frac{1}{2}(L_+ + L_-)[/tex]

[tex]\psi = \sum \alpha_{lm} Y_{lm}[/tex]

3. The attempt at a solution

I understand how to get the expectation value of [itex]L_x[/itex] for the entire wavefunction through the inner product [itex]\langle \psi |L_x| \psi \rangle[/itex] and how to get the Fourier coefficients for the state probabilities, but I don't see how to get the "possible outcomes". Expectation values of individual eigenstates [itex]\langle Y_{lm} |L_x| L_{lm} \rangle[/itex] are always equal to 0, so I don't see how you can measure any outcome but 0 for definite eigenstates. Shouldn't the only outcome be the expectation value of the entire wavefunction?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Possible outcomes of angular momentum state

**Physics Forums | Science Articles, Homework Help, Discussion**