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Have multi-particle state of full Hamiltonian and one-particle state of free Hamiltonian non-zero scalar product? Intuitively one can say that scalar product of such states should be zero because each of these states mentioned above belongs to different (orthogonal) subspaces of the Fock space.

Do you know any reference discussing this problem?

P.S. these states are eigenvectors of appropriate Hamiltonians

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# [Quick] States of interacting and non-interacting Hamiltonian

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