This equation is missing a sum symbol, also it should be e^(-iEt/ℏ), where in the correct case the amplitude does not change. What you get is a sum of products of each occupied stationary state and a time-dependent phase. So the general solution looks like this:
Indeed. But as another commenter points out, what I think they wanted was to solve only for eigenstates here. Apparently I'm not the only one this confused.
This equation is missing a sum symbol, also it should be e^(-iEt/ℏ), where in the correct case the amplitude does not change. What you get is a sum of products of each occupied stationary state and a time-dependent phase. So the general solution looks like this:
https://en.wikipedia.org/w/index.php?title=User:Scythe33/san...