Scattering Matrix: Solve 1D Schrodinger Equation

[genius2687]

Homework Statement

We are interested in the solution of the Schrödinger equation with positive energy E = h_^2k^2/2m for the potential V(x) = -v_0*delta(x). We take the scattering state under the form Ae^ikx+Be^-ikx for x<0, and Ce^ikx+De^-ikx for x>0

Find the scattering matrix S(k)

Homework Equations

S(k)-1/(2ik) = f(k).

The Attempt at a Solution

I'm not sure where to start here. How do you find the scattering matrix for a 1-D case? I know how do do it for a 3D case.

 

[Meir Achuz]

In 1D, "scattering matrix" means the reflection and transmission coefficients
R and T. The wave function for x>0, should be only Cexp{+ikx}.