NationMaster - Encyclopedia: Transmission coefficient (physics)

The transmission coefficient, $left| frac{C_{mbox{outgoing}}}{C_{mbox{incoming}}} right|^2$ , for a particle tunneling through a single barrier potential is found to be: This article is about the transmission coefficient in optics. ...

$T = frac{e^{-2int_{x_1}^{x_2} dx sqrt{frac{2m}{hbar^2} left( V(x) - E right)}}}{ left( 1 + frac{1}{4} e^{-2int_{x_1}^{x_2} dx sqrt{frac{2m}{hbar^2} left( V(x) - E right)}} right)^2}$

Where $x 1, x 2$ are the 2 classical turning points for the potential barrier. If we take the classical limit of all other physical parameters much larger than Planck's constant, abbreviated as $hbar rightarrow 0$ , we see that the transmission coefficient correctly goes to zero. This classical limit would have failed in the unphysical, but much simpler to solve, situation of a square potential.

If the transmission coefficient is much less than 1, it can be approximated with the following formula:

is the length of the barrier potential.

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