[tex] u(r,\theta,\phi)=R(r) Y(\theta,\phi)[/tex](adsbygoogle = window.adsbygoogle || []).push({});

Where Y is the spherical harmonics

[tex] \frac{\partial^2 Y}{\partial \theta^2} + cot\theta \frac{\partial Y}{\partial \theta} + csc^2 \frac{\partial^2 Y}{\partial \phi^2} + \mu Y = 0[/tex]

The book said this equation has nontrivial solutions when

[tex]\mu = \mu_n = n(n+1) \hbox { , for } n=0,1,2.......[/tex]

Can anyone explain why?

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# Help with Differential equation for Spherical Harmonics.

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