1. Solve the TISE in each region to find the stationary wave function, and show that it can be written as
?(x) = Ae^{ikx }+(k-1)/(k+1)Ae^{ikx }x<0
=2k/(k+1)Ae^{ilx} x>0
where A represents the amplitude of the incoming wave and k and l are constants which depend on the energy.
I think I have this question OK.
2. Find an expression for the electron's position probability distribution, and sketch it, indicating the magnitudes of key features in terms of the variables A, k, and l where possible.
Here I get
A^{2} [1+2(k-1)/(k+1) cos(2kx) +((k-1)/(k+1))^{2} + (2k/k+1)^{2}]
from
?*?(x<0)+?*?(x>0).