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

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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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olgranpappy
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well... yeah. if it is time dependent then it is not time-independent... so all time dependent solutions are not time-independent solutions.
 
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yea but without the time dependence factor (t=0), wouldnt they be time independent too?
 
olgranpappy
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yea but without the time dependence factor (t=0), wouldnt they be time independent too?
yes, but without the time-dependent factor then it is not the same function. in general the time-dependence doesn't factor.
 
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the time independant schrodinger equation only applies when you can use seperation of variables, while you could theoretically apply it at t=0 and get basis states for that particular instant, this would be of little use as the time evolution would be completely different.

so if you have a solution to the time independant equation this means the solution can be put in the form of e^(-iEt)y(x) whereas you can't do this for a solution to the time dependant solution
 
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Asked my teacher and found out that linear combination of separable states as solution to SE dont apply to the time independent SE but only to the time dependent SE. Not even at t=0.
 
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