I'm reading some course notes for a physics class that contain the following step in a derivation:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\phi(\vec{x}) = \int \frac{d^3k}{(2\pi)^3}\frac{e^{i\vec{k}\cdot\vec{x}}}{\vec{x}^2 + m^2}[/itex]

Changing to polar coordinates, and writing [itex]\vec{k}\cdot\vec{x}=kr \cos\theta[/itex], we have:

[itex]\phi(\vec{x}) = \frac{1}{(2\pi)^2} \int_0^\infty dk \frac{k^2}{k^2 + m^2}\frac{2\sin kr}{kr}[/itex]

I'm having a bit of difficulty seeing this step. Could someone please show some of the intermediate steps between these two and explain what's happening? I understand that k^{2}in the numerator comes from converting to spherical coordinates, but that's about all I follow.

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

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

# Stuck on a change of variables

Loading...

Similar Threads for Stuck change variables |
---|

I Dx as a small change in x |

I Rate of change of area under curve f(x) = f(x) |

I Function of 2 variables, max/min test, D=0 and linear dependence |

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