Dirac delta distribution: Difference between revisions
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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> | ||
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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]] | |||
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,
![{\displaystyle {\frac {d}{dx}}[H(x)]=\delta (x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f2c48a895b8b4a9377436f7331790b8f5fc356aa)
It has the property
