I recently read a bit about the Schrodinger picture in QFT and wavefunctionals, see e.g. Polchinski's String Theory lectures, and I wanted to ask if the intuitive understanding of QFT I got is "right". I understood that a state in quantum field theory is very similar to the state in usual QM: There, a particle may be at any position in the configuration space, and the wavefunction give's a probability amplitude to every such configuration. In QFT, a field can be in any classical state $\phi(x)$, and these are weighted with the amplitude of the wave-functional $\Psi[\phi(x)]$. I also read that a QFT state may be written as $\int D\phi \Psi[\phi(x)]|\phi(x)\rangle$, where the $|\phi(x)\rangle$ are similar to position eigenstates in QM states which correspond to classical field configurations. But how do I construct these eigenstates $|\phi(x)\rangle$? Does something like $$|\phi(\vec x,t)\rangle=\int d^3x \phi(\vec x,t) \Phi(\vec x) |0\rangle$$ work, where $\Phi(x)$ shall be the Schrodinger field operator which creates a particle localized at position $\vec x$?