Homework Help: Spherical Harmonics/Angular Momentum

1. Oct 19, 2011

atomicpedals

1. The problem statement, all variables and given/known data

Given that Lz(x+iy)m=m$\hbar$(x+iy)m. Show that L+=(x+iy)m.

2. The attempt at a solution

I'm probably grasping at straws here, but when I see the expression for Lz I instantly go to Lz|lm>=m$\hbar$|lm>. This then leads me to suspect that |lm>=(x+iy)m. Is this correct, and how on Earth does it get me any closer to what I want to show for the raising operator?

2. Oct 23, 2011

vela

Staff Emeritus
Not exactly. What $\hat{L}_z(x+iy)^m=\hbar m(x+iy)^m$ tells you is that $(x+iy)^m \propto \langle x,y | l~m \rangle$. You need to keep the distinction between kets and the representation of the ket in some basis. Writing $(x+iy)^m = |l~m\rangle$ is, at best, a terrible abuse of notation.

I have no idea what $\hat{L}_+ = (x+iy)^m$ is supposed to mean.