1. Consider a cubic box with infinitely high walls at side lengths Lx = Ly = Lz = L. (a) Write an expression for the potential energy. (b) Write the Schrdinger equation in 3D Cartesian coordinates for the inside of the box. (c) Separate the 3D Schrdinger equation into three independent 1D Schrdinger equations. (d) Derive the expression for the wavefunctions and energy levels for the particle in a cubic box using the 1D particle-in-a-box solutions. (e) State which states (if any) are degenerate with the nx=1,ny=2,nz=1 state. (f) Without any calculations, determine the expectation values of position in each direction (hxi, hyi, and hzi).