Classical limit of Bose--Einstein and Fermi--Dirac statistics

When

E - μ ≫ k_{B} T

, the additive

\mp 1

is negligible and both quantum distributions reduce to the Maxwell--Boltzmann factor

e^{- (E - μ) / (k_{B} T)}

.

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- Nonrelativistic Maxwell--Boltzmann number density Classical limit of Bose--Einstein and Fermi--Dirac statistics

Nonrelativistic Maxwell--Boltzmann number density

For particles of mass

m

, spin degeneracy

g_{s}

m c^{2} + p^{2} / (2 m)

,

n = g_{s} (\frac{2 πm k _{B} T}{h ^{2}})^{3/2} e^{(μ - m c^{2}) / (k_{B} T)} .

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