# What is $[\mathrm{J}]$ supposed to denote in this case?

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.

• It means (1.2) is expressed in Joules. Dec 7, 2020 at 3:25
• @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? Dec 7, 2020 at 3:25
• 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. Dec 7, 2020 at 4:03
• The [J] is pointless and confusing, since equations like 1.2 are true in any units. Dec 7, 2020 at 4:22
• Clearly there's a typo somewhere as $h\nu \ne h c/\nu$. I think the last one should be $h c/\lambda$ since $\lambda \nu =c$. Dec 7, 2020 at 5:11

$$E_p = E_2 - E_1 = h \nu = \dfrac{h c}{\lambda} \ \ \ \ \ \ \ [\mathrm{J}] \tag{1.2}$$ where $$h = 6.626 \times 10^{-34}$$ J-sec is Planck’s constant.
$$E_p/J = E_2 - E_1 = h \nu = \dfrac{h c}{\lambda} \ \ \ \ \ \ \ \tag{1.3}.$$
It means that $$E_p$$ is expressed in units of $$Joules$$, so $$E_p/J$$ is $$E_p$$ per unit $$J$$.