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I am currently studying Laser Systems Engineering by Keith Kasunic. Chapter 1.2 Laser Engineering says the following:

If the energy of the incident electromagnetic field more-or-less matches that of the electron’s excited state energy $E_2$ compared with some lower-energy state $E_1$, then there is a high probability the electron will give up its energy in the form of a stimulated photon whose energy $E_p$ in Fig. 1.9(a) is $$E_p = E_2 - E_1 = h \nu = \dfrac{h c}{\lambda} \ \ \ \ \ \ \ [\mathrm{J}] \tag{1.2}$$ where $h = 6.626 \times 10^{-34}$ J-sec is Planck’s constant.

What is $[\mathrm{J}]$ supposed to denote in this case? I read this relevant question on square brackets in dimensional analysis, but I don't think it clarifies what it means in this particular case.

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    $\begingroup$ It means (1.2) is expressed in Joules. $\endgroup$ Dec 7, 2020 at 3:25
  • $\begingroup$ @ZeroTheHero That's all? There isn't some additional meaning given by the square brackets? Why wouldn't the author just leave it as $\mathrm{J}$, then? $\endgroup$ Dec 7, 2020 at 3:25
  • $\begingroup$ depends on the authors I guess. It's sometimes indicated so that in particular the value of hbar is taken to be in correct numerical value in Joules. $\endgroup$ Dec 7, 2020 at 4:03
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    $\begingroup$ The [J] is pointless and confusing, since equations like 1.2 are true in any units. $\endgroup$
    – G. Smith
    Dec 7, 2020 at 4:22
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    $\begingroup$ Clearly there's a typo somewhere as $h\nu \ne h c/\nu$. I think the last one should be $h c/\lambda$ since $\lambda \nu =c$. $\endgroup$ Dec 7, 2020 at 5:11

1 Answer 1

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$$E_p = E_2 - E_1 = h \nu = \dfrac{h c}{\lambda} \ \ \ \ \ \ \ [\mathrm{J}] \tag{1.2}$$ where $h = 6.626 \times 10^{-34}$ J-sec is Planck’s constant.

Another way of writing this is,

$$E_p/J = E_2 - E_1 = h \nu = \dfrac{h c}{\lambda} \ \ \ \ \ \ \ \tag{1.3}.$$

It means that $E_p$ is expressed in units of $Joules$, so $E_p/J$ is $E_p$ per unit $J$.

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