We have a potential structure as follows: from z=negative infinity to z=-b, the potential is 0. At z=-b, the potential jumps up to some V_0. Then, at z=0, there is a potential barrier of infinite height. I need to solve for the magnitude of the reflected wave (i.e. the wave propagating to the left). Assume that E is greater than V_0.
We know that to the left, where the potential is 0, the wavefunction has the from Aexp(ikz) + Bexp(-ikz), where k=sqrt(2mE)/h-bar. To the right, where the potential is equal to V_0, the wavefunction is of the form Csin(fz), where f=-sqrt(2m(E-V_0))/h-bar.
The Attempt at a Solution
I'm really unsure. I know that we have the boundary conditions at z=-b, that the wavefunction has to be continuous and the derivative has to be continuous as well. It get's really messy though, because z=-b, and not 0. The TA also told us to utilize the fact that the probability over the entire region (from negative infinity to 0) is 1. Problem is though, I'm having trouble normalizing everything. Anybody have any ideas?