In the case of an element producing white light, it is possible that the bandwidth of the quantum as suggested in end of the post "Mood Stone", is itself wide enough to contain the whole spectrum. This bandwidth is the result of the electron and another valence electron from its neighboring atom both performing SHM about its radius \(r_e\), as such pushing and stretching their \(r_e\) vs \(T\) profile. The band gap is changed continuously and as a result the quantum spread over a range of frequency. Calcium is such an element.
In this case, green light will still reflect green, as the amount of energy transferred to the electron depended on the photon, electrons that fail to reach the kink with enough energy will not emit any quantum. But the reflection will contain a fair amount of white light, that result from the band gap changing dynamically. A prism in the path of green light reflecting off a white calcium surface will show this.
Moreover, light dispersion occurs in all material and in the reflection there will be lower frequency components (post "Light Dispersion?)'. For green incident light, yellow can be seen. A green light incident-ed on a white surface obliquely, shows yellow on the far edge of the incident spot.
Still, there is this problem of photons themselves not being the quanta. If photon energy can be parceled and dispensed, can photon absorb a quantum directly? And transport the quantum along its way?
A photon bus! A photon is self-propelling; to light speed or terminal velocity of free space.
