Oscillators in a black body (electrons) can only have energy equal to $E = nhf$ ie it is a linear relationship. so if an electron drops from energy level $n$ to a lower energy (jumping 1, 2,3 ... shells) this I believe the energy is proportional to $1/n^2$. how do these ideas coexist?
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Oscillators in the sense of material systems considered to make up a black body are not electrons, or atoms with electrons. They are an abstract description of matter, a (very) simplifying replacement of the complicated system of immense number of nuclei and electrons, with dense and complicated energy level structure.
When atoms are so close to each other as in a solid body, they no longer have simple energy spectrum we use to describe rarified emitting gas, like $E_n = - K/n^2$ for hydrogen , but instead the whole system (of many atoms) has very dense, sometimes called "quasi-continuous", spectrum of energy levels. This is because of the mutual interaction between the atoms - it destroys degeneracy, causes splitting of the few discrete levels, valid when atoms are far apart, into very many dense levels, valid when atoms are densely packed.
Matter made of (quantum) harmonic oscillators is just the simplest mathematical model of a solid interacting with equilibrium radiation to analyze in quantum theory - and it can lead to the correct formula for spectrum of radiation, so people use it. This is so already from the times of Max Planck (who however preferred to think of the matter system as made of many classical harmonic oscillators with continuously changing energy, which he called "resonators").
Ján Lalinský
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