(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known

A general one dimensional scattering problem could be characterized by an

(arbitrary) potential V (x) which is localized by the requirement that V (x) = 0

for |x|> a. Assume that the wave-function is

ψ (x) =

Ae^(ikx) + Be^(-ikx) x < -a

Ce^(ikx) + De^(-ikx) x > a

Relating the \outgoing" waves to the \incoming" waves by the matrix equation

C=S11A+ S12B

B=S21A+ S22D

show that

|S11|^2 + |S21|^2 = 1

|S12|^2 + |S22|^2 = 1

S11S12* + S21S22* = 0

Use this to show that the S matrix is unitary.

2. Relevant equations

I don't understand why C=S11A+S12B or B=S21A+S22D

3. The attempt at a solution

I calculate the flux for the incoming beam and the outgoing beam and set them equal, i get 2A^2 ik-2ikB^2=2C^2ik-2D^2ik i don't see how C and B can be expressed with only two other variables.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: One dimension scattering problem

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