Wavefunction DFT (Mathematica)

[algorhythmic]

This question is not directly related to QM although my reason for asking it is I'm trying to compute wavefunctions on my PC -- please excuse me if this is the wrong place to ask. I am having trouble using the DFT in Mathematica although I don't think my problem is directly Mathematica related.

My problem is that the DFT is not giving me the output I expect, i.e. the output that I get if I take the analytical FT.

In the following images I have the wavefunction as given and compute the CFT and DFT:

CFT : http://imgur.com/WxMTl,ROzWg#1
DFT : http://imgur.com/WxMTl,ROzWg#0

As you can see the although the DFT is correctly normalized to 1, it is incorrectly scaled. If I change the parameters n1 (steps) or L (domain) then this scaling is affected.
I need to do something to get the Fourier[] DFT function to know about the value dx. I have tried adjusting the FourierParemeters option for Fourier and have spent a great amount of time without finding a solution to what seems to be a very simple problem.

Any help would be *greatly* appreciated.

Thanks.

 

[brydustin]

What sort of answer are you looking for, and what do you think that the solution should be? In other words, are you certain that Mathematica is right but that you might be looking at it in a different light. I find this happens a lot with Mathematica; often, I will use it (or Wolfram Alpha) and when I solve an entire solution I will get the more elegant expression as a result (the kind that I would not compute by hand), then I do the steps (in Mathematica) and get a "different" answer (that I would get if I did on paper) and its equivalent.