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.