Fourier Transform of Gaussian Function

1. Oct 20, 2008

TheDestroyer

Hello guys,

I have got a homework for Advanced Quantum Mechanics, actually I've tried to solve it in many ways my own, but I'm always forced to use computer at the end (For infinite series or improper integrals), I want to solve it my self, so I can do it also in the class!

The problem is:

Find the fourier transform of exp((a x^2)/2)

Actually the first way I tried is by splitting the fourier factor exp(ikx) to sine and cosine, by Euler form, but no use! because I reached "Abramowitz and Stegun integral", which have a result without details.

The second way is in the PDF, where I tried to release the exp((a x^2)/2) term to an infinite series, But also no use, I reached the Erf error function due to an infinite series!!!!

2. Oct 20, 2008

olgranpappy

Try completeing the square in the exponent...

;)

3. Oct 20, 2008

TheDestroyer

You mean in the PDF? or from the begining?

4. Oct 20, 2008

TheDestroyer

Sorry, I didn't understand how can this benefit me, If I completed the square this will cause the appearance of a new exponential multiplicand!!!

I also failed because in the first term inside the exponential I have a, and in the second no a! so how can I do it?

5. Oct 21, 2008

TheDestroyer

Why you guys aren't helping? Is the question too difficult? or I don't deserve the help??

6. Oct 21, 2008

olgranpappy

calm down. I'm not online 24 hours a day. You completed the square in the exponent of the integrand of the fourier transform and what did you end up with. Show up your work, if possible. Also, if possible can you write your work down using LaTeX.

7. Oct 21, 2008

TheDestroyer

Thank you :), It's solved, I succeeded, my mistake was in the completion of the square using variables, I used the constants and it worked ;)

Thanks :)