1. (20 points) Starting from the expression for PA(I): 35 + 65 1 90 compute (using appropriate formulae from the tutorial; you must show your work for credit ) the spherical harmonic Y (0,4). 2. (10 bonus points) What is the eigenvalue of YA (0, 4) under the operator L3? 3. (20 points) Separate the three dimensional wave equation, in spherical coordinates. You may assume azimuthal symmetry. You do not need to solve the radial or time equations, but you should write down or describe the solutions to the 0 equation. (20 points) Consider a thin spherical shell of radius a, centered at the origin. The electrostatic potential on its surface is given by Vrea - Vo (cos0 | sin' 0 sin 24)