A particle with mass m and energy E is inside a square with tube infinite potential barriers at x=0, x=a, y=0 and y=a. The tube is infinitely long in the z direction. Inside the tube v=0. The particle is moving in the +z direction solve the Schrodinger equation to derive the allowed wave functions for this particle. Do not try to normalize the wave functions, but make sure they correspond to motion in the +z direction.