Distribution function (physics): Difference between revisions

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:''This article describes the ''distribution function'' as used in physics. You may be looking for the related mathematical concepts of [[cumulative distribution function]] or [[probability density function]].''

{{Unreferenced|date=December 2009}}

:''This article describes the ''distribution function'' as used in physics. You may be looking for the related mathematical concepts of [[cumulative distribution function]] or [[probability density function]].''

In molecular [[kinetic theory of gases|kinetic theory]] in [[physics]], a particle's '''distribution function''' is a function of seven variables, <math>f(x,y,z,t;v_x,v_y,v_z)</math>, which gives the number of particles per unit volume in single-particle [[phase space]]. It is the number of particles per unit volume having approximately the [[velocity]] <math>(v_x,v_y,v_z)</math> near the place <math>(x,y,z)</math> and time <math>(t)</math>. The usual normalization of the distribution function is

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:<math>N(t) = \int n \,dx \,dy \,dz, </math>

where, ''N'' is the total number of particles, and ''n'' is the [[number density]] of particles  – the number of particles per unit volume, or the [[density]] divided by the mass of individual particles.

A distribution function may be specialised with respect to a particular set of dimensions. E.g. take the quantum mechanical six-dimensional phase space, <math>f(x,y,z;p_x,p_y,p_z)</math> and multiply by the total space volume, to give the momentum distribution, i.e. the number of particles in the momentum phase space having approximately the [[momentum]] <math>(p_x,p_y,p_z)</math>.