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I have a question about the concept of complete set when I apply the perturbation theory in two situations -Finite Hilbert Space and Infinite Hilbert Space.

Consider a Hamiltonian H=H0+H', where H0 is the unperturbed Hamiltonian and H' is the perturbed Hamiltonian. Let ψ_n be the complete set of unperturbed Hamiltonian H0.

Do ψ_n still constitute a complete set of the overall Hamiltonian H for either finite Hilbert space or infinite Hilbert space if the perturbed Hamiltonian is turned on?

Ck

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# Finite Hilbert Space v.s Infinite Hilbert Space in Perturbation Theory

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