Editing Normal distribution (section)

=== Exact normality ===
[[File:QHarmonicOscillator.png|thumb|The ground state of a [[quantum harmonic oscillator]] has the Gaussian distribution.]]
Certain quantities in [[physics]] are distributed normally, as was first demonstrated by [[James Clerk Maxwell]]. Examples of such quantities are:
* Probability density function of a ground state in a [[quantum harmonic oscillator]].
* The position of a particle that experiences [[diffusion]]. If initially the particle is located at a specific point (that is its probability distribution is the [[Dirac delta function]]), then after time ''t'' its location is described by a normal distribution with variance ''t'', which satisfies the [[diffusion equation]]&nbsp;<math display=inline>\frac{\partial}{\partial t} f(x,t) = \frac{1}{2} \frac{\partial^2}{\partial x^2} f(x,t)</math>. If the initial location is given by a certain density function <math display=inline>g(x)</math>, then the density at time ''t'' is the [[convolution]] of ''g'' and the normal probability density function.