1: A hard wall A free quantum particle with kinetic energy E}; and mass m is incident from the right (large x) onto a hard wall at z = a, and reflects back to the right. (a) In the region x > a, show that the free particle wave function is a solution to the Schrodinger equation. (b) What are the units, if any, for the wave function? (c) Using the exponential form from the previous problem set, 2($) Azeikx ke Bzet'k:r, find k in terms of Ej and m. Which term is the left and which is the right traveling wave? (d) What boundary condition does the wall at = a impose on the free particle wavefunction (state the condition mathematically). Find a condition between A, and By which ensures that the wavefunction satisfies your boundary condition. (e) Repeat your calculation using the sin and cosine form of the free particle solution, 1(z) = Ay sin(kzx) + By cos(kz). Using your result from the previous problem set, are these two wavefunctions, 1(z) and 9(z) equivalent