Laplace's Equation in Polar Coordinates

• Central Forces 2021
  1. Write down Laplace's equation in two dimensions in polar coordinates.
  2. Use the separation of variables procedure to separate this partial differential equation into two ordinary differential equations.
  3. Write down a complete set of eigenstates of the \(\phi\) equation. Justify your answer. You do not NEED to calculate anything here, but if you quote some answer that you already know, say how/where you know the answer. DO NOT TRY TO SOLVE THE \(r\) EQUATION!