Hence, ik−[ψ+(xa)−ψ−(xa)]=ik+[ψ+(xb)−ψ−(xb)]. These two equations can be combined into a single matrix equation: \[\begin{bmatrix}1 & 1 \\ k...Hence, ik−[ψ+(xa)−ψ−(xa)]=ik+[ψ+(xb)−ψ−(xb)]. These two equations can be combined into a single matrix equation: [11k−−k−][ψ+(xa)ψ−(xa)]=[11k+−k+][ψ+(xb)ψ−(xb)]. After doing a matrix inversion, this becomes \[\Psi_b = \mathbf{M}_s(k_+,k_-) \, \Psi_a, \;\;\;\mathrm{where}\…
ϕI(x)=A0eik0x+B0e−ik0x,ϕII(x)=A1eik1x. We define a transmission (T) and reflection (R...\boldsymbol{\begin{align} ϕ_I (x) &= A 0 e^{ i k_0 x} + B_0 e^{ − i k_0 x} , \label{6.7} \\[5pt] ϕ_{II} (x) &= A_1 e^{ i k_1 x} . \label{6.8} \end{align}} We define a transmission (T) and reflection (R) coefficient as the ratio of currents between reflected or transmitted wave and the incoming wave, where we have canceled a common factor A1=2k0k0+k1A0B0=k0−k1k0+k1A0,
