Dirac delta distribution: Difference between revisions
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:<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]] | [[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,
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{d}{dx}[H(x)] = \delta(x)}
It has the property
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int_{- \infty}^{\infty} f(x) \delta (x-a) dx = f(a)}