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## Main Question or Discussion Point

I know in ordinary QM, the spectrum of the Hamiltonian [itex]\{ E_{n}\}[/itex] gives you just about everything you need for the system in question (roughly speaking). So what happens to this spectrum in QFT where [itex]|\psi\rangle[/itex] is now a multiparticle wavefunction in some Fock space? I've been trying to understand this, but I don't yet have a clear grasp. Essentially, what's wrong with writing [itex]\hat H |\psi_{n}\rangle=E_{n}|\psi_{n}\rangle[/itex] in QFT where the psi's are now multiparticle states?