(adsbygoogle = window.adsbygoogle || []).push({}); A solution to time dependent SE but not Time independent SE??

How is it possible that a wave function is a solution to the time dependent schroedinger equation, but not to the time independent schroedinger equation (without time factors tacked on) with the same potential? I had this case on my quantum physics exam. I wrote that the time dependent set consisted of a linear combination of wavefunctions which were solutions from another potential which spanned hilbert space. But it still sounds contradicting that this function didnt fit into the time independent schroedinger equation when its basis functions span the space too.

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# A solution to time dependent SE but not Time independent SE?

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