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Q1. A particle in an infinite tube.
a) 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 substantially long in the z direction. Inside the tube v=0. The particle is moving in the +z direction solve the Schrodinger equation to obtain the allowed wave functions for this particle. Do not try to normalize wave functions, but make sure they correspond to motion in the +z direction.
b) Energy must not be quantized in this case because the particle is not in a bound state. Use the answer from part a to show that this is indeed the case.
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