deletions | additions       diff --git a/untitled.tex b/untitled.tex  index fc465be..127341d 100644  --- a/untitled.tex  +++ b/untitled.tex 
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\[\begin{bmatrix} \tilde{A}(z)\\  \tilde{B}(z)\\  \end{bmatrix}=\begin{bmatrix}  \frac{\beta_c \frac{\tilde{A}(0) \beta_c  cos \beta_c(z)-i\delta sin \beta_c(z)}{\beta_c}e^{i \delta (z)} & 0\\ \tilde{A}(0)  \frac{i \kappa_{ba}}{\beta_c}sin\beta_c(z)e^{-i \delta (z)} & 0\\ \end{bmatrix} \]  This leaves us then with \[\tilde{A}(z)=\tilde{A}(0)\left( cos \beta_c z -\frac{i \delta}{\beta_c} sin \beta_c z \right) e^{i \delta z} \]  \[\tilde{B}(z)=\tilde{A}(0)\left(\frac{i \kappa_{ba}}{\beta_c} sin \beta_c z \right) e^{-i \delta z} \]