Potential Step and Wave Functions

[DunceMoin]

Homework Statement

Homework Equations

The Attempt at a Solution

For x>b, Ψ(x) = Ae^-ikx + Be^ikx , where k = (√2mE)/hbar
a<x<b Ψ(x) = Ce^-ik'x + De^ik'x , where k = (√2m(U₂ - E)/hbar

This is the problem part
0<x<a Ψ(x) = Fsink''x , where k = (√2m(E+U₁)/hbar
I think this should be a standing wave, but am not sure if I am correct or not as I've never encountered a question like this before.

x<0 Ψ(x) = 0

 

[DunceMoin]

Sorry for the missing image. http://postimg.org/image/kvjgg1nh3/

 

[Sergey Vilov]

I think you solution is correct. As concerns the standing wave, note that the spatial wave function should be multiplied by exp(-iwt) with w=E/hbar in order to get the solution to the Shrodinger equation. This will give you a standing wave.