TDSWE: Deriving Time Dependent Solutions from TISWE

[jaydnul]

Maybe I'm missing something in my book, but it seems to me that the only importance of the time dependent SWE was to derive the time independent SWE. Is it true that in all cases you just need to solve the TISWE and then to find the time dependence, you tack on the $e^{\frac{-iE_nt}{hbar}}$ and sum all the linear combinations for the general solution?

Or can this method only be done for a time independent potential?

 

[jtbell]

Or can this method only be done for a time independent potential?

That is correct. You generally cannot use the "separation of variables" method on the time-dependent SE if the potential energy function depends on time.