Statistical thermodynamics MOC

Bose-Einstein statistics

Bose-Einstein statistics is applicable to a system of 𝑁 identical and indistinguishable bosons, i.e. particles not obeying the Pauli exclusion principle and thus able to occupy the same states. A unique microstate is therefore labelled by every combination of occupation numbers 𝐾𝑖 for each particle state |𝑖⟩, such that all occupation numbers add to 𝑁 =∑𝑖𝐾𝑖

⃗𝐊∈BE={⃗𝐊∈(ℕ0)𝑁:∑𝑖𝐾𝑖=𝑁}

and the energy of such a microstate is given by

𝐸⃗𝐊=∑𝑖𝐾𝑖𝜀𝑖=⃗𝐊⋅⃗𝜀

Hence the canonical partition function is given by

𝑍=∑⃗𝐊∈BEexp⁡(−⃗𝐊⋅⃗𝜀𝑘𝐵𝑇)

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