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If we have a system with hamiltonian $H = H_{0} + H_{I}$, the Gell-Mann and Low theorem allow us to relate the exact state $\Psi$ of the interacting system with the ground state $\phi_{0}$ of the system without the interaction $H_{I}$. Here, $\phi_{0}$ is a eigenstate of $H_{0}$. However, This theorem is applicable only for normalizable states. But what happen if the $H_{0}$ hamiltonian has a continuum spectra and $\phi_{0}$ is not normalized? Is the theorem appliable yet?

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