In quantum optics we quantize the electromagnetic field and describe it using the harmonic oscillator model and the formalism of annihilation and creation operators. For the electric field operator we find for example for a single mode $$ E(z,t) \propto \sin(kz)\cdot q(t) $$ and a similar expression for the magnetic field which has a time dependence $p(t)$. From the operators $q$ and $p$ we define the annihilation and creation operators and the quadrature operators.
However, I have been wondering about the role of the eigenfunctions of the harmonic oscillators for this model.
In the classical harmonic oscillator $p$ and $q$ correspond to the momentum and position of the particle over time, whereas they are only operators in quantum optics. The states of the electromagnetic field, for example $|n \rangle$. "We" never actually looked at the wave function that would correspond to that state. Is there a physical meaning to the wave functions?