# Raising momentum operator acting on spherical harmonics

1. Dec 7, 2009

### FourierX

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

What is the result of raising momentum ladder operator (L+) acting on spherical harmonics Y04 ($$\theta$$,$$\phi$$)

2. Relevant equations

3. The attempt at a solution

I was expecting Y14 ($$\theta$$,$$\phi$$)

I applied L+ on Y04 ($$\theta$$,$$\phi$$) and ended up with Y14 ($$\theta$$,$$\phi$$) multiplied by $$\sqrt{20}$$h-bar.

Thanks in advance

2. Dec 7, 2009

### jdwood983

That is what you should get:

$$L_+Y_\ell^m=\hbar\sqrt{(\ell-m)(\ell+m+1)}Y_\ell^{m+1}$$

with $\ell=4$ and $m=1$, you get

$$L_+Y_4^0(\theta,\phi)=\hbar\sqrt{20}Y_4^1(\theta,\phi)$$

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