Having taking courses in both physics and nuclear engineering, I've noticed that the two fields tend to describe photons/light in two different settings.
In nuclear engineering, the radiative transfer equation (Boltzmann transport equation for photons) is often used. For example, as noted in the Wikipedia article, simulations for radiation therapy treatments solve this equation to model the dose applied to a patient. From what I understand, this equation treats light essentially as particles.
In another more physics/E&M-oriented class that I'm taking, light is described via the Maxwell equations. I'm not a physicist so I don't know that much about those equations, but it seems like it's an entirely unrelated/different approach for describing light. Here, it seems like light is treated more as a wave as opposed to particles. In this class I'm taking, we see that, under certain assumptions, the Maxwell equations eventually lead to a Helmholtz equation, which seems very different from the Boltzmann transport equation. (For starters, there's a second order spatial derivative instead of a first-order derivative.)
Can someone help me reconcile the two approaches? i.e., how is it that we can look at light from such drastically different points of view? I know that there's the whole thing about light being both a particle and a wave, but I don't see how the two approaches are even related. Are there certain frequency ranges where the transport equation is more applicable or something?
Any relevant references or explanations would be appreciated. Thanks!