Raising momentum operator acting on spherical harmonics

[FourierX]

Homework Statement

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

Homework Equations

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

 

[jdwood983]

That is what you should get:

<br /> L_+Y_\ell^m=\hbar\sqrt{(\ell-m)(\ell+m+1)}Y_\ell^{m+1}<br />

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

<br /> L_+Y_4^0(\theta,\phi)=\hbar\sqrt{20}Y_4^1(\theta,\phi)<br />