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Do we then know that the wave function describing the electron is an eigenstate of the Hamiltonian? The question arose because I was given a problem where the intial wave function was a linear combination of eigenstates, which I guess is perfectly possible. But then I thought: Did God create this state or was it created because we had some potential from outside which put it there and was then turned off.

It seems that for all practical calculations you always assume that the electrons are described by their corresponding eigenstates (free electron gas etc. etc.)