Dirac delta distribution: Difference between revisions
Jump to navigation
Jump to search
Carl McBride (talk | contribs) No edit summary |
Carl McBride (talk | contribs) m (Added applications section.) |
||
(2 intermediate revisions by 2 users not shown) | |||
Line 1: | Line 1: | ||
The Dirac delta distribution (or generalized function) is written as <math>\delta(x)</math>. It is the derivative of the [[Heaviside step distribution]], | The '''Dirac delta distribution''' (or generalized function) is written as <math>\delta(x)</math>. It is the derivative of the [[Heaviside step distribution]], | ||
:<math>\frac{d}{dx}[H(x)] = \delta(x)</math> | :<math>\frac{d}{dx}[H(x)] = \delta(x)</math> | ||
Line 6: | Line 6: | ||
:<math>\int_{- \infty}^{\infty} f(x) \delta (x-a) dx = f(a)</math> | :<math>\int_{- \infty}^{\infty} f(x) \delta (x-a) dx = f(a)</math> | ||
==Applications in statistical mechanics== | |||
*[[1-dimensional hard rods]] | |||
[[category: mathematics]] |
Latest revision as of 10:59, 7 July 2008
The Dirac delta distribution (or generalized function) is written as . It is the derivative of the Heaviside step distribution,
It has the property