I am trying to prove that when applying the inverse QFT to the following state:
we get the following result:
However, I get a wrong prefactor. Can anyone tell me where I went wrong? Here my calculations:
Here, the last equality comes by realizing that y is an integer and thus all terms of the second bracket give 1. The first bracket can be evaluated as follows:
Then we can plug in:
Obviously I should get 1/sqrt(r) not sqrt(r), but I don't find my mistake...