Spherical harmonics

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Homework Statement



Finding the potential.

Homework Equations



general solution of potential is in terms of spherical harmonics Y_l,m.

The Attempt at a Solution



My question is how do we know which l to choose given a boundry condition. for example if the potenial on the surface of a sphere of radius "a" = const*sin (theta) cos(theta). How do we know which l that corresonds to? or do we try all the l's and see which one works out?

Thanks
 

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