Difference between revisions of "Talk:DWBA"

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(Simplification)
(Simplification)
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= \,\, & T_i^2 T_f^2 | F(+Q_{z1}) |^2 + T_i^2 R_f^2 | F(-Q_{z2}) |^2 + R_i^2 T_f^2 | F(+Q_{z2}) |^2 + R_i^2 R_f^2 | F(-Q_{z1}) |^2 \\
 
= \,\, & T_i^2 T_f^2 | F(+Q_{z1}) |^2 + T_i^2 R_f^2 | F(-Q_{z2}) |^2 + R_i^2 T_f^2 | F(+Q_{z2}) |^2 + R_i^2 R_f^2 | F(-Q_{z1}) |^2 \\
 
         & + 2 \times T_i^2T_fR_f F(+Q_{z1})F(-Q_{z2}) \\
 
         & + 2 \times T_i^2T_fR_f F(+Q_{z1})F(-Q_{z2}) \\
         & + 2 \times T_iR_iT_f^2 F(+Q_{z1})F(-Q_{z2}) \\
+
         & + 2 \times T_iR_iT_f^2 F(+Q_{z1})F(+Q_{z2}) \\
 
         & + 2 \times T_i R_i T_f R_f [ F(+Q_{z1})F(-Q_{z1}) + F(+Q_{z2})F(-Q_{z2}) ]  \\
 
         & + 2 \times T_i R_i T_f R_f [ F(+Q_{z1})F(-Q_{z1}) + F(+Q_{z2})F(-Q_{z2}) ]  \\
 
         & + 2 \times T_iR_iR_f^2 F(-Q_{z1})F(-Q_{z2}) \\
 
         & + 2 \times T_iR_iR_f^2 F(-Q_{z1})F(-Q_{z2}) \\
Line 89: Line 89:
 
= \,\, & T_i^2 T_f^2 | F(+Q_{z1}) |^2 + T_i^2 R_f^2 | F(-Q_{z2}) |^2 + R_i^2 T_f^2 | F(+Q_{z2}) |^2 + R_i^2 R_f^2 | F(-Q_{z1}) |^2 \\
 
= \,\, & T_i^2 T_f^2 | F(+Q_{z1}) |^2 + T_i^2 R_f^2 | F(-Q_{z2}) |^2 + R_i^2 T_f^2 | F(+Q_{z2}) |^2 + R_i^2 R_f^2 | F(-Q_{z1}) |^2 \\
 
         & + 2 \times T_i^2T_fR_f F(+Q_{z1})F(-Q_{z2})  
 
         & + 2 \times T_i^2T_fR_f F(+Q_{z1})F(-Q_{z2})  
           + 2 \times T_iR_iT_f^2 F(+Q_{z1})F(-Q_{z2}) \\
+
           + 2 \times T_iR_iT_f^2 F(+Q_{z1})F(+Q_{z2}) \\
 
         & + 2 \times T_i R_i T_f R_f [ F(+Q_{z1})F(-Q_{z1}) + F(+Q_{z2})F(-Q_{z2}) ]  \\
 
         & + 2 \times T_i R_i T_f R_f [ F(+Q_{z1})F(-Q_{z1}) + F(+Q_{z2})F(-Q_{z2}) ]  \\
 
         & + 2 \times T_iR_iR_f^2 F(-Q_{z1})F(-Q_{z2})  
 
         & + 2 \times T_iR_iR_f^2 F(-Q_{z1})F(-Q_{z2})  
Line 105: Line 105:
 
= \,\, & T_i^2 T_f^2 | F_{+1} |^2 + T_i^2 R_f^2 | F_{-2} |^2 + R_i^2 T_f^2 | F_{+2} |^2 + R_i^2 R_f^2 | F_{-1} |^2 \\
 
= \,\, & T_i^2 T_f^2 | F_{+1} |^2 + T_i^2 R_f^2 | F_{-2} |^2 + R_i^2 T_f^2 | F_{+2} |^2 + R_i^2 R_f^2 | F_{-1} |^2 \\
 
         & + 2 \times T_i^2T_fR_f F_{+1}F_{-2}  
 
         & + 2 \times T_i^2T_fR_f F_{+1}F_{-2}  
           + 2 \times T_iR_iT_f^2 F_{+1}F_{-2} \\
+
           + 2 \times T_iR_iT_f^2 F_{+1}F_{+2} \\
 
         & + 2 \times T_i R_i T_f R_f [ F_{+1}F_{-1} + F_{+2}F_{-2} ]  \\
 
         & + 2 \times T_i R_i T_f R_f [ F_{+1}F_{-1} + F_{+2}F_{-2} ]  \\
 
         & + 2 \times T_iR_iR_f^2 F_{-1}F_{-2}
 
         & + 2 \times T_iR_iR_f^2 F_{-1}F_{-2}

Revision as of 10:06, 7 March 2018

DWBA Equation in thin film

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

Expansion

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 :