# Homework Help: Derivative of Spherical Harmonic for negative m

1. Mar 8, 2014

### VVS

Hello!

1. The problem statement, all variables and given/known data
I want to evaluate the derivative of spherical harmonics with respect to the azimuthal angle and express it in terms of spherical harmonics.

2. Relevant equations and 3. The attempt at a solution
I have calculated the derivative of the spherical harmonic with respect to the azimuthal angle.
I know how to express the derivative of the spherical harmonic in terms of spherical harmonics for positive m. But I don't know how to do this for negative m.

View attachment Spherical_Harmonics.pdf

2. Mar 8, 2014

### Jufro

Isn't the azimuthal angle the argument of the Exp[], in this case θ?

3. Mar 8, 2014

### VVS

Yes you're right. I meant that I want the derivative wrt the polar angle.

4. Mar 8, 2014

### Jufro

Hope this is what you were looking for.

It isn't the final answer because you can still express Cot ø and Exp(iθ) in terms of the spherical harmonics but that part is not the worst. May even be able to find them in a table somewhere.

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5. Mar 8, 2014

### VVS

Hello!

Yes!! That is exactly what I was looking for.
Although I recalculated it and I get a slightly different result.
I will upload my calculations tomorrow or so. Right now I am too tired.

thanks

6. Mar 10, 2014