# Bose-Einstein statistics

(Redirected from Bose–Einstein statistics)

In statistical mechanics, Bose-Einstein statistics means the statistics of a system where you can not tell the difference between any of the particles, and the particles are bosons. Bosons are fundamental particles like the photon.[1]

The Bose-Einstein distribution tells you how many particles have a certain energy. The formula is

${\displaystyle n(\varepsilon )={\frac {1}{e^{(\varepsilon -\mu )/kT}-1}}}$

with ${\displaystyle \varepsilon >\mu }$ and where:

n(ε)  is the number of particles which have energy ε
ε  is the energy
μ is the chemical potential
k is Boltzmann's constant
T is the temperature

If ${\displaystyle \varepsilon -\mu \gg kT}$, then the Maxwell–Boltzmann statistics is a good approximation.

## References

• Griffiths, David J. (2005). Introduction to quantum mechanics (2nd ed.). Upper Saddle River, NJ: Pearson, Prentice Hall. ISBN 0131911759.

## Notes

1. Bosons have integer (whole number) spin and the Pauli exclusion principle is not true for them.