Dirac Delta Function

$\delta (x-x_0)=\frac{1}{2\pi }{\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}d\kappa \exp (i\kappa (x-x_0))$

${\int }_{\mathbb{R}}\delta (x-x_0)f(q)dq=f(x_0)$

• $\delta (k)=\frac{1}{2\pi }{\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}dx\exp (\pm ikx)$