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So basically I want to find the Eigenfunctions and Energies of a quantized electromagnetic field which is perturbed under a pertubation Hamiltonian. The Hamiltonian can be expressed something like this (ignoring polarization) $\sum_{k} \hbar \omega_k (a^\dagger_{k}a_k+1/2)+H_{perturbed}(a^\dagger_k,a_k)$ But to begin using the equations presented by Landau&Lifschitz in Quantum Mechanics. I need the eigenfunctions of the Hamiltonian! But I have no clue what these are, since these are many Harmonic Oscillators. Are the eigenfunctions just superpositions of many harmonic oscillators? Please help me.

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