- $\ddot u (t) +\omega^2u(t) -\gamma\dddot u = f(t)\approx \sin(\omega t)$,
The dynamics of near-resonance is quite subtle as explained in detail on Computational Blackbody Radiation showing that Planck's constant enters as a parameter in a high-frequency cut-off reflecting Wien's displacement law.
- $ih\dot\psi = E\psi$,
- $\psi (t) =\exp(i\omega t) =\cos(\omega t)+i\sin(\omega t)$,
- Blackbody radiation is a near-resonance phenomenon of molecules or collections of atoms modeled as a forced harmonic oscillator with small damping. Collections of atoms vibrate without electron configurations changing energy.
- Atomic radiation is a direct resonance phenomenon which can be modeled by a harmonic oscillator. Electrons oscillate between two energy levels representing eigenstates of an atom.
The value of $h$ as setting a conversion scale between light energy and electronic energy can be determined by the photoelectric effect and can then be used by definition in blackbody radiation and Schrödinger's equation.