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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  Comparison of average occupancy of the ground state for three statistics

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