(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[itex] \phi\left(x,t\right)=\frac{1}{2\pi}\int^{\infty}_{-\infty}e^\left(i\left(xk-tk^2\right)\right)dk[/itex]

2. Relevant equations

Solve for [itex] \phi [/itex] analytically

3. The attempt at a solution

completing the square of the exponent to give me

[itex] \phi\left(x,t\right)=\frac{1}{2\pi}\int^{\infty}_{-\infty}e^\left(-ti\left(k^2-\frac{x}{t}k + \frac{x^2}{4t^2} - \frac{x^2}{4t^2}\right)\right)dk [/itex]

Simplifying I get

[itex] \phi\left(x,t\right)=\frac{e^\frac{x^2}{4t}}{2\pi}\int^{\infty}_{-\infty}e^\left(-ti\left(k-\frac{x}{2t}\right)^2\right)dk [/itex]

From here I don't know

tried u substitution

[itex] u=k-\frac{x}{2t} , du=dk [/itex]

but this gets me nowhere

any help is appreciated

**Physics Forums | Science Articles, Homework Help, Discussion**

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!

# Homework Help: Solving a difficult integral

**Physics Forums | Science Articles, Homework Help, Discussion**