Abstract
The study of particle system is inevitable to study its statistical law, and understanding the distribution of particles is fundamental and important. In this paper, the author points out the relation between the number of states of free particles in the relativistic and non-relativistic cases, and gives formulae for each case. Furthermore, the author enumerates some popular and basic particle systems, as well as classifies them in terms of relativistic and non-relativistic cases, also their basic formulae are deduced and enumerated in this paper. These particle systems are applicable to different formulae for the density of states for relativistic or non-relativistic cases. It is concluded that the different densities of states in different cases are related to each other through the de Broglie relation and the energy formula.
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