- #1

mantysa

- 1

- 0

[tex]\nabla^2 f=0[/tex]

I know that in spherical coordinates this equation may be decomposed into two equations,

first which depends only on r, and the second one which has the form of spherical harmonics equation except that the [tex]l(l+1)[/tex] is an arbitrary constant, let's say C (and of course the same constant is present in the first equation).

I do not understand why we consider (in literature for example) only the case of

[tex]C=l(l+1)[/tex]

What if we have an equation of form:

[tex]\left(\frac{1}{\sin\theta}\frac{\partial}{\partial\theta}\sin\theta\frac{\partial}{\partial\theta}+\frac{1}{\sin^2\theta}\frac{\partial^2}{\partial\phi^2}+C\right)u=0[/tex]

is any way to decompose [tex]u[/tex] into spherical harmonics or to transform this equation into standard spherical harmonic equation?