a.) A particle of mass m and energy E is inside a square tube with 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 but make sure they correspond to motion in the +z direction.
b.) Energy should not be quantized in this case because the particle is not in a bound state. Use the answer from a.) to show that this is indeed the case.