(adsbygoogle = window.adsbygoogle || []).push({}); 1 = 0 <-- What goes fundamentally wrong? Delta distribution

[itex]2 \pi a = \iint \delta(a^2 - (x^2+y^2)) \mathrm d x \mathrm d y [/itex]

Differentiating both sides w.r.t. "a" (using chain rule on the RHS) gives

[itex]\frac{\pi}{a} = \iint \delta'(a^2 - (x^2+y^2)) \mathrm d x \mathrm d y[/itex]

Changing variables (and noting that integrand is independent of theta)

[itex]\frac{\pi}{a} =2 \pi \int \delta'(a^2 - r^2) \cdot r \cdot \mathrm d r [/itex]

Eliminate the pi on both sides, but more importantly we can rewrite the RHS as (using chain rule!)

[itex]\frac{1}{a} = - \int \frac{\partial}{\partial r} \delta(a^2 - r^2) \mathrm d r[/itex]

However the RHS is obviously zero, explicitly: [itex]0= \delta(a^2-r^2) \big|_{r=0}^{r=+\infty}[/itex].

DISCLAIMER: I know I use the delta as a physicist would, but please be flexible... I would really appreciate knowing where itessentiallygoes wrong.

**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!

# 1 = 0 <- What goes fundamentally wrong? Delta distribution

Loading...

Similar Threads - goes fundamentally wrong | Date |
---|---|

I Fundamental elements transformation | May 29, 2017 |

Curvature of a circle approaches zero as radius goes to infinity | Apr 15, 2014 |

Function/Curve that goes through certain points? | Mar 10, 2014 |

\sum 1/log(n) goes like ? | Aug 14, 2011 |

What goes into a capable math mind? | Aug 9, 2011 |

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