I have encountered an exercise question asking the reader to verify that a wavefunction is normalized. So I calculated the probability density -- $|{\psi}|^2$, then verified that the integral does indeed give 1. So all is well. But then the questions asks the reader to find the probability density! (I presume that means that one doesn't have to find the prob density to do the verification.) So I am wondering if there are other, perhaps quicker, ways to check that a wavefunction is normalized.
In case it is relevant, the wavefunction in the question is $\psi(x,t)=\frac{1}{(1-it)^\frac{1}{2}\pi^\frac{1}{4}}e^\frac{-x^2}{2(1-it)}$. This in itself is actually pretty easy to evaluate...! So I wonder if there really is an easier way.
Thanks.