# Spherical Harmonic Question

1. May 16, 2008

### architect

Spherical Harmonic Question!!!

Hi,

I have a spherical harmonic which is a function of $$\theta$$ and $$\phi$$, written as $$Y_n_m(\theta,\phi)$$. I recently found an equation which is written as follows:

$$Y_n_m(\frac{x_2 - x_1}{\left\|x_2 - x_1\right\|})$$

I am trying to understand its meaning in order to include it in my simulations. Note that in my case $$\theta = \pi/2$$ so the vectors become 2-dimensional.

I know that in order to evaluate a Spherical Harmonic we need a value for $$\theta$$ and a value for $$\phi$$. As I can understand from the equation above, the $$\frac{x_2 - x_1}{\left\|x_2 - x_1\right\|}$$ term will produce a new normalized vector, that is the difference between $$x_2 - x_1$$. In my case the points/vectors are located on a circle (not inside the circle) of some radius R.

The author of the book mentions that the magnitude is $$\left\|x_2 - x_1\right\| = 0.1,0.2,...2$$, in steps of 0.1. My problem is that I want to evaluate the Spherical Harmonic for all the values of $$\left\|x_2 - x_1\right\| = 0.1,0.2,...2$$ but I cannot see how to do it since the input to the spherical harmonic is the angle $$(\theta=\pi/2, \phi)$$. Knowing that $$\left\|x_2 - x_1\right\| = 0.1,0.2,...2$$ does not tell me anything about $$x_2 - x_1$$ or DOES IT???

I would appreciate someone's help

Thanks

Regards

Alex