Difference between revisions of "Talk:DWBA"

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(Expansion)
(Terms)
Line 121: Line 121:
  
 
\begin{matrix}
 
\begin{matrix}
           &  (T_i^* T_f^*)     &  (T_i^* R_f^*)      &  (R_i^* T_f^*)    &  (R_i^* R_f^*)    \\
+
           &  (T_i^* T_f^*)       &  (T_i^* R_f^*)      &  (R_i^* T_f^*)    &  (R_i^* R_f^*)    \\
(T_i T_f)  &  T_i T_i^* T_f T_f^*   &  T_i T_i^* T_f R_f^*  & T_i R_i^* T_f T_f^*    &  T_i R_i^* T_f R_f^*  \\
+
(T_i T_f)  &  T_i T_i^* T_f T_f^* &  T_i T_i^* T_f R_f^*  & T_i R_i^* T_f T_f^*    &  T_i R_i^* T_f R_f^*  \\
(T_i R_f)  &  T_i T_i^* T_f^* R_f   &  T_i Ti^* R_f R_f^*    &  T_iR_iT_fR_f T_iR_iR_f^2   \\
+
(T_i R_f)  &  T_i T_i^* T_f^* R_f &  T_i Ti^* R_f R_f^*    &  T_i R_i^* T_f^* R_f T_i R_i^* R_f R_f^*   \\
(R_i T_f)  &  T_i^* R_i T_f T_f^*   T_iR_iT_fR_f   &  R_i R_i^* T_f T_f^*    &  R_i^2T_fR_f   \\
+
(R_i T_f)  &  T_i^* R_i T_f T_f^* T_i^* R_i T_f R_f^*   &  R_i R_i^* T_f T_f^*    &  R_i R_i^* T_f R_f^*   \\
(R_i R_f)  &  T_i^* R_i T_f^* R_f  &  T_iR_iR_f^2   &  R_i^2T_fR_f   &  R_i R_i^* R_f R_f^*    \\
+
(R_i R_f)  &  T_i^* R_i T_f^* R_f  &  T_i^* R_i R_f R_f^*   &  R_i R_i^* T_f^* R_f   &  R_i R_i^* R_f R_f^*    \\
 
\end{matrix}
 
\end{matrix}
  

Revision as of 18:36, 12 March 2018

DWBA Equation in thin film

Using the notation for compactness, the DWBA equation inside a thin film can be written:

Expansion (incorrect)

WARNING: This incorrectly ignores the complex components.

Terms

If one expands the of the DWBA, one obtains 16 terms:

Equation

The equation can thus be expanded as:

Simplification

We can rearrange to:


We can rewrite in a more compact form using the notation and :

Expansion

Terms

If one expands the of the DWBA, one obtains 16 terms:

Breaking into components

The experimental data can be broken into contributions from the transmitted channel and reflected channel :

We define the ratio between the channels to be:

Such that one can compute the two components from:

and: