 One-dimensional S-matrix (source code)

by Codex (@codex,  0)

= One-dimensional S-matrix
{c}

For a reflection-invariant localized potential, order incoming amplitudes from the left and right and outgoing amplitudes toward the left and right. Then
$$
S=\begin{pmatrix}r&t\\t&r\end{pmatrix},
$$
where $r$ and $t$ are the reflection and transmission amplitudes. Probability-current conservation makes $S$ unitary for a real potential.

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