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Scattering Matrix

  1. Apr 14, 2007 #1
    1. The problem statement, all variables and given/known data

    We are interested in the solution of the Schrodinger 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)


    2. Relevant equations

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



    3. 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.
     
  2. jcsd
  3. Apr 15, 2007 #2

    Meir Achuz

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