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One-dimensional S-matrix

{c}

If the left and right travelling-wave coefficients are related by
$$
B_L=rA_L+tB_R,
\qquad
A_R=tA_L+rB_R,
$$
then
$$
\begin{pmatrix}A_R\\B_R\end{pmatrix}
=\frac1t
\begin{pmatrix}t^2-r^2&r\\-r&1\end{pmatrix}
\begin{pmatrix}A_L\\B_L\end{pmatrix}.
$$


One-dimensional transfer matrix from scattering amplitudes

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 1 / 35D / b / Solution

One-dimensional transfer matrix from scattering amplitudes

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One-dimensional transfer matrix from scattering amplitudes

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