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Wikipedia https://en.wikipedia.org/wiki/Semiconductor_optical_gain proposes the following formula for the material gain in semi-conductor:

$$ g(\varepsilon) = \frac{\nu\mu_0^2}{4\pi\epsilon_0n} \left(\frac{2m_r}{\hbar}\right)^{3/2}\sqrt\varepsilon $$

where $\nu$ a frequency, $\mu_0$ a dipole moment, $\epsilon_0$ the permittivty of vaccum, n the refractive index (non dimensional), $m_r$ is a reduced mass and $\varepsilon$ the energy at which it is computed.

The result is supposed to be in $m^{-1}$ but a dimensional analysis shows that this is in $s^{-1}$.

I wonder if the result should have been divided by $c$ for it to work?

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  • $\begingroup$ There is something to be fixed in the equation for $g(\epsilon)$ with respect to Wikipedia's one. $\endgroup$
    – Jon
    Jun 13, 2017 at 12:16
  • $\begingroup$ Should not it be $\hbar^2$ without $\sqrt{\epsilon}$? Otherwise this seems your formula and you should explain how did you obtain it. $\endgroup$
    – Jon
    Jun 13, 2017 at 12:28

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