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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.

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    You _do_ need to calculate the prob. density $|\psi(x,t)|^2$ and do the integral in order to check the normalization, so you've done the right thing. In fact, because of the complex standard deviation, calculating the integral properly takes some extra work (compared to the real case, where it's just a matter of identifying $\sigma$); maybe the first question only asked to do so at $t = 0$?2011-08-25
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    Thanks, Gerben. Weirdly enough, the question doesn't ask for a $t=0$ case... Silly question... :P At least now I know that it's not me missing something.2011-08-25
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    @H Taylor: if somehow you're not sure about your approach, you can always post your solution and have us check it for you.2011-08-27

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