For the simple quantum harmonic oscillator we can solve Schrodinger's equation and derive the analytic form of the eigenstates of e.g. a non relativistic electron in a harmonic potential. We may then go on to define ladder operators which enable us to move between eigenstates of the potential. One interpretation of these ladder operators is that they 'create' or 'destroy' a photon of energy hw. One can go on to define the Number operator which enables us to determine how many times the oscillator has been excited or equivalently how many 'photons' there are in the system.
My question is: is it correct to say the wavefunction we derived for the different energy levels still just describes the single non-relativistic electron and doesn't describe the newly created/destroyed photons.
If this is correct then where does the interpretation of 'creation' of particles even come from because it seems like we are not describing the produced photons with any wavefunction we are merely postulating that they have been created? What is a good intuitive explanation for the interpretation in terms of photon creation?