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

[Pyrus96]

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.

 

[blue_leaf77]

Do all physical states, ψ, abide to Hψ = Eψ

Not all, only eigenstates of the (time-independent) Hamiltonian satisfy that equation.