# Robinett's fourier transform

1. Sep 16, 2007

### ehrenfest

1. The problem statement, all variables and given/known data
Richard Robinett defined the Fourier transform with an exp(-ikx) and the inverse Fourier transform with an exp(ikx). I have always seen the opposite convention and I thought it was not even a convention but a necessity to do it the other in order to apply it to some Gaussian equations. Has anyone ever seen this sign convention before?

2. Relevant equations

3. The attempt at a solution

2. Sep 16, 2007

### dextercioby

It really isn't relevant whether it's with a plus, or with a minus. I've seen in most cases

$$\phi (x)=\frac{1}{(2\pi)^{3/2}}\int dk \ \tilde{\phi}(k) e^{-ikx}$$.

3. Sep 16, 2007

### HallsofIvy

Note that the integration is from $-\infty$ to $\infty$. That's why the sign does not matter.

4. Sep 16, 2007

### genneth

Furthermore, the constants in front also do not really matter, as long as they combine to give 1/(2 pi). There are a couple of theorems which depend on them (I think Parseval's theorem and the associated ones do), but it's all up to a constant. My supervisor (in physics) recommends just ignoring the constants, and adding them back in if you have to at the end

5. Sep 16, 2007

### Jimmy Snyder

If you define the Fourier transform as dextercioby did:
$$\phi (x)=\frac{1}{(2\pi)^{3/2}}\int dk \phi(k) e^{-ikx}$$
then the inverse transform is:
$$\phi (k)=\frac{1}{(2\pi)^{3/2}}\int dx \phi(x) e^{ikx}$$
It is merely a matter of convention which is called which. There's no 'wrong' convention as long as you remain consistent.

On page 11 of 'Photons and Atoms' by Claude Cohen-Tannoudji et. al. the convention above is used. On page 97 of 'The Principles of QM' by P.A.M. Dirac, the convention is left deliciously ambiguous.

Last edited: Sep 16, 2007