1.Show that the spherical harmonic functions are eigenfunctions of the Laplacian operator for l=0 and l=1. What are the associate eigenvalues?
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The eigenvalue equation is given by: $\nabla^2 Y_{lm}(\theta, \phi) = -\frac{l(l+1)}{r^2} Y_{lm}(\theta, \phi)$ where $l$ is the azimuthal quantum number and $m$ is the magnetic quantum number. The eigenvalues are $-\frac{l(l+1)}{r^2}$. Show more…
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