Do All Physical States Satisfy the Hamiltonian Equation Hψ = Eψ?

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SUMMARY

Only eigenstates of the time-independent Hamiltonian satisfy the equation Hψ = Eψ. This conclusion is based on the fundamental principles of quantum mechanics, where physical states that are not eigenstates do not fulfill the Hamiltonian equation. The discussion clarifies that the Hamiltonian operator, H, acts on these eigenstates, yielding the corresponding energy eigenvalues, E.

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I came across a previous exam question which stated: Do all physical states, ψ, abide to Hψ = Eψ. I thought about it for a while, but I'm not really sure.
 
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Pyrus96 said:
Do all physical states, ψ, abide to Hψ = Eψ
Not all, only eigenstates of the (time-independent) Hamiltonian satisfy that equation.
 
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