Statistical thermodynamics MOC

Fermi-Dirac statistics

Fermi-Dirac statistics is applicable to a system of 𝑁 identical and indistinguishable fermions, i.e. particles obeying the Pauli exclusion principle and thus unable to occupy the same states. A unique microstate is therefore labelled by every combination of occupation numbers 𝐾𝑖 ∈{0,1} for each particle state |𝑖⟩, such that all occupation numbers add to 𝑁 =∑𝑖𝐾𝑖,

⃗𝐊∈FD={⃗𝐊∈{0,1}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∈FDexp⁡(−⃗𝐊⋅⃗𝜀𝑘𝐵𝑇)

---

develop | en | SemBr