My name is Alexander FufaeV and here I will explain the following topic:

# Bose Distribution: The Occupation Probability of Bosons

## Formula

What do the formula symbols mean?

## Probability

Unit
The occupation probability indicates with which probability $$P$$ a state with energy $$W$$ at temperature $$T$$ is occupied by a boson (for example a photon or phonon).

## Energy

Unit
Energy state which can be occupied by a boson, for example by a photon or $$^4\text{He}$$ atom.

## Chemical potential

Unit
Chemical potential indicates the change of internal energy when the particle number of the boson gas changes. At $$T = 0$$ the chemical potential corresponds to the Fermi energy.

## Temperature

Unit
Absolute temperature of the boson gas (for example a photon gas).

## Boltzmann Constant

Unit
Boltzmann constant is a physical constant from many-particle physics and has the following exact value: $$k_{\text B} ~=~ 1.380 \, 649 ~\cdot~ 10^{-23} \, \frac{\mathrm{J}}{\mathrm{K}}$$
Explanation

## Video

The Bose distribution (also called Bose-Einstein distribution) indicates the occupation probability $$P(W)$$ that a boson in a system takes on the energy $$W$$. The occupation probability depends on the temperature $$T$$ of the system.

Formula anchor

The crucial difference to the Boltzmann distribution is the presence of the term "-1" in the denominator, which ensures that the probability of occupying energy states does not become infinitely large when the temperature approaches zero. This leads to Bose-Einstein condensation, in which bosons can occupy the same energetic ground state at very low temperatures.