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Matteo Cantiello edited Magnetic Trapping.tex
about 9 years ago
Commit id: af8066a776973ec98c78515b07a949bdf2826c66
deletions | additions
diff --git a/Magnetic Trapping.tex b/Magnetic Trapping.tex
index c077973..26401f7 100644
--- a/Magnetic Trapping.tex
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The degree of reflection is determined by the tunneling integral through the evanescent region. The transmission coefficient is
\begin{equation}\label{eq:integral}
T = \exp{\int^{r_2}_{r_1} i k_r dr} \simeq \exp{\int^{r_2}_{r_1} -
\frac{\sqrt{ \ell ( \ell +1)}}{r} \frac{\sqrt{l(l+1)}}{r} dr } \, ,
\end{equation}
where $r_1$ and $r_2$ are the boundaries of the evanescent region (in this case, the upper boundary occurs where $\omega