Dirac Delta Function
Definition
\(\delta(x-x_0) = \frac{1}{2\pi}\int_{-\infty}^\infty d\kappa\exp(i\kappa(x-x_0))\)
\(\int_\mathbb{R}\delta(x-x_0)f(q)dq = f(x_0)\)
Representations
- \(\delta(k)=\frac{1}{2\pi}\int_{-\infty}^\infty dx\exp(\pm ikx)\)
\(\delta(x-x_0) = \frac{1}{2\pi}\int_{-\infty}^\infty d\kappa\exp(i\kappa(x-x_0))\)
\(\int_\mathbb{R}\delta(x-x_0)f(q)dq = f(x_0)\)
Created: 2023-06-25 Sun 02:35