Dirac delta distribution

The Dirac delta distribution (or generalized function) is written as $\delta (x)$. 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)}

Applications in statistical mechanics

• 1-dimensional hard rods