## Disclaimer

This site as of now just a technology demonstration and its claims should not be taken as true (even though I myself am pretty confident they are)

## Laplace equation

Solutions to this equation are called harmonics

## Laplace equation in spherical coordinates

Using the definition for the laplace operator in spherical coordinates, it follows:

Using sepration of variables becomes

Applying this to the original equation produces

Because the terms depend on different independant variables, the only way the equation holds is if both terms are constant.

## Angle dependant term

We again use separation of variables to solve the partial differential equation of the angle dependant term.

Replacing into the equation

Based on a similar argument it follows that both terms must be constant, with this we may now solve for

Solve using Frobenius Method