(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that the spherical harmonic wave function [tex] \frac{1}{r}e^{i(kr-{\omega}t)} [/tex] is a solution of the three-dimensional wave equation, where [tex] r = (x^2+y^2+z^2)^{\frac{1}{2}} [/tex]. The proof is easier if spherical coordinates are used.

2. Relevant equations

Wave function: [tex] \frac{{\partial}^2U}{\partial x^2} + \frac{{\partial}^2U}{\partial y^2} + \frac{{\partial}^2U}{\partial z^2} = \frac{1}{u^2} \frac{{\partial}^2U}{\partial t^2}[/tex]

3. The attempt at a solution

I really just don't even know where to start. Do I first convert the x,y,z into polar coordinates? or do I just substitue what's above in for r? But then what's up with imaginary part?

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# Spherical Harmonic Wave Function =? 3D Wave Function

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