This comes from quantum mechanics but it's basically a Fourier integral I can't quite do...(adsbygoogle = window.adsbygoogle || []).push({});

F(k) = 1/sqrt(2a*[pi]) * [inte] exp( -(ax^2+ikx) dx over infinite limits. i is sqrt(-1)

to do this, I complete the square getting

exp( -(sqrt(a)*(x +ik/(2a))^2 * exp(k^2 / (4a))

sticking this in the integral and integrating over x I get

F(k) = 1/sqrt(2a*[pi]) * exp(k^2 / 4a )

I like the k^2 / a part but the factor of 4 seems wrong as well as the sign of the exponent possibly.

exp(-a x^2) should transform to exp(k^2/a)?

Help with using completing the square to do this integral would be greatly appreciated.

I used [inte] exp(-y^2) = sqrt([pi]) from a table.

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Hellp with fourier integral via completing the square

Loading...

Similar Threads for Hellp fourier integral | Date |
---|---|

A Getting a finite result from a non-converging integral | Thursday at 6:32 PM |

I Repetitive Fourier transform | Apr 2, 2018 |

I Units of Fourier Transform | Mar 26, 2018 |

A Help with Discrete Sine Transform | Sep 29, 2017 |

**Physics Forums - The Fusion of Science and Community**