Advanced Search

Question: Laplace on Spherical Harmonics mess instead of -l(l+1)Y_lm. How to simplify?

Question:Laplace on Spherical Harmonics mess instead of -l(l+1)Y_lm. How to simplify?

bogo 55
operator vectorcalculus
February 18 2015
2

Its a well known fact that the spherical harmonics are eigenfunctions of the Laplace operator on the unit sphere with eigenvalues -l(l+1). Its used all over the place in QM for example. However maple does not seem to have this. 

with(VectorCalculus)

 

SetCoordinates('spherical'[r, theta, phi])

 

Laplacian(SphericalY(l, m, theta, phi))

 

 

Try it, you might be surprised. Its going to be a mess. How do you deal with it, to simplify it to the known form -l(l+1)r-2Ylm??
Please Wait...