Difference between revisions of "DPL94 math"
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<math> | <math> | ||
\sin^2\theta \left( \frac{\Phi_\textrm{ex} \textrm{k}_\textrm{ex}}{\textrm{k}_\textrm{ex}^2 + \omega_\textrm{e}^2} \right) = | \sin^2\theta \left( \frac{\Phi_\textrm{ex} \textrm{k}_\textrm{ex}}{\textrm{k}_\textrm{ex}^2 + \omega_\textrm{e}^2} \right) = | ||
| − | \frac{w_\textrm{1}^2}{w_\textrm{eff}^2} \cdot \left( \frac{\Phi_\textrm{ex} \textrm{k}_\textrm{ex}}{\textrm{k}_\textrm{ex}^2 + w_\textrm{1}^2 + \Omega^2} \right) | + | \frac{w_\textrm{1}^2}{w_\textrm{eff}^2} \cdot \left( \frac{\Phi_\textrm{ex} \textrm{k}_\textrm{ex}}{\textrm{k}_\textrm{ex}^2 + w_\textrm{1}^2 + \Omega^2} \right) = |
| + | \frac{w_\textrm{1}^2}{\textrm{k}_\textrm{ex}^2 + w_\textrm{1}^2 + \Omega^2} \cdot \left( \frac{\Phi_\textrm{ex} \textrm{k}_\textrm{ex}}{\textrm{k}_\textrm{ex}^2 + w_\textrm{1}^2 + \Omega^2} \right) | ||
</math> | </math> | ||
Revision as of 11:42, 20 March 2014
Equation
[math] \mathrm{R}_{1\rho}= \mathrm{R}_1\cos^2\theta + \left( \mathrm{R}_{1\rho}{´} + \frac{\Phi_\textrm{ex} \textrm{k}_\textrm{ex}}{\textrm{k}_\textrm{ex}^2 + \omega_\textrm{e}^2} \right) \sin^2\theta [/math]
Expressing in terms of $\textrm{w}_\textrm{1}, \textrm{w}_\textrm{eff}$
[math]
\sin^2\theta \left( \frac{\Phi_\textrm{ex} \textrm{k}_\textrm{ex}}{\textrm{k}_\textrm{ex}^2 + \omega_\textrm{e}^2} \right) =
\frac{w_\textrm{1}^2}{w_\textrm{eff}^2} \cdot \left( \frac{\Phi_\textrm{ex} \textrm{k}_\textrm{ex}}{\textrm{k}_\textrm{ex}^2 + w_\textrm{1}^2 + \Omega^2} \right) =
\frac{w_\textrm{1}^2}{\textrm{k}_\textrm{ex}^2 + w_\textrm{1}^2 + \Omega^2} \cdot \left( \frac{\Phi_\textrm{ex} \textrm{k}_\textrm{ex}}{\textrm{k}_\textrm{ex}^2 + w_\textrm{1}^2 + \Omega^2} \right)
[/math]
