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.

Q2. Standing at a crosswalk, you hear a frequency of 580 Hz from the siren of an approaching ambulance. After the ambulance passes, the observed frequency of the siren is 493 Hz. Conclude the ambulance's speeds from these observations.