Editing S-matrix (section)

=== Transmission coefficient and reflection coefficient ===
The [[transmission coefficient]] from the left of the potential barrier is, when {{math|1=''D'' = 0}},
<math display="block">T_{\rm L}=\frac{|C|^2}{|A|^2} = |S_{21}|^2. </math>

The [[reflection coefficient]] from the left of the potential barrier is, when {{math|1=''D'' = 0}},
<math display="block">R_{\rm L}=\frac{|B|^2}{|A|^2}=|S_{11}|^2.</math>

Similarly, the transmission coefficient from the right of the potential barrier is, when {{math|1=''A'' = 0}},
<math display="block">T_{\rm R}=\frac{|B|^2}{|D|^2}=|S_{12}|^2.</math>

The reflection coefficient from the right of the potential barrier is, when {{math|1=''A'' = 0}},
<math display="block">R_{\rm R}=\frac{|C|^2}{|D|^2}=|S_{22}|^2.</math>

The relations between the transmission and reflection coefficients are
<math display="block">T_{\rm L}+R_{\rm L}=1</math>
and
<math display="block">T_{\rm R}+R_{\rm R}=1.</math>
This identity is a consequence of the unitarity property of the ''S''-matrix.

With time-reversal symmetry, the S-matrix is symmetric and hence <math>T_{\rm L}=|S_{21}|^2=|S_{12}|^2=T_{\rm R}</math> and <math>R_{\rm L} = R_{\rm R}</math>.