Maxwellian Distribution, Maxwell-Boltzmann Distribution

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Maxwell-Boltzmann Distribution Equation

For particles in a classical gas at a temperature, $T$, the statistical distribution of velocities is given by

\[
f(v) = \frac{4}{\sqrt{\pi}}\left(\frac{m}{2kT}\right)^{\frac{3}{2}}
v^{2} \exp{(-mv^{2}/2kT)}.
\]

It is known by various names, most commonly Maxwellian distribution, Maxwell-Boltzmann distribution. It is nonrelativistic, applying only to a classical gas.