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.

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

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

with [math]\displaystyle{ \varepsilon \gt \mu }[/math] 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 [math]\displaystyle{ \varepsilon-\mu \gg kT }[/math], then the Maxwell–Boltzmann statistics is a good approximation.

Bose-Einstein Statistics Media

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  Equilibrium thermal distributions for particles with integer spin (bosons), half integer spin (fermions), and classical (spinless) particles. Average occupancy \langle n\rangle is shown versus energy \epsilon relative to the system chemical potential \mu, where T is the system temperature, and k_\text{B} is the Boltzmann constant.

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  The image represents one possible distribution of bosonic particles in different boxes. The box partitions (green) can be moved around to change the size of the boxes and as a result of the number of bosons each box can contain.

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  The image represents one possible distribution of bosonic particles in different boxes. The box partitions (green) can be moved around to change the size of the boxes and as a result of the number of bosons each box can contain.

References

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