Fermi–Dirac Distribution for Non-interacting Fermions

The Fermi–Dirac distribution describes how particles are distributed over energy states in systems consisting of many identical particles that obey the Pauli exclusion principle.

The occupation number is directly proportional to the particle spin, and inversely proportional to 1 plus the exponential of the difference betweeen state energy and the chemical potential per mole times the number of moles, all divided by the Boltzmann constant and the temperature.

Formula

QuantityVariable[OverBar[Subscript["n", "i"]], "Unitless"] == (1 + 2*QuantityVariable["s", "Unitless"])/(1 + E^((Quantity[1, "BoltzmannConstant"^(-1)]*(-(QuantityVariable["n", "Amount"]*QuantityVariable["μ", "ChemicalPotential"]) + QuantityVariable[Subscript["E", "i"], "Energy"]))/QuantityVariable["T", "Temperature"]))

Forms

Examples

Open in Wolfram Cloud

Download Example Notebook

Get the resource:

In[1]:=

$ResourceObject["Fermi\[Dash]Dirac Distribution for Non-interacting \ Fermions"]$

Out[1]=

Get the formula:

In[2]:=

$FormulaData[ ResourceObject[ "Fermi\[Dash]Dirac Distribution for Non-interacting Fermions"]]$

Out[2]=

Use some values:

In[3]:=

$FormulaData[ ResourceObject[ "Fermi\[Dash]Dirac Distribution for Non-interacting Fermions"], \ {QuantityVariable["n","Amount"] -> Quantity[1, "Moles"]}]$

Out[3]=

Wolfram Formula Repository (Under Development)

Fermi–Dirac Distribution for Non-interacting Fermions

Formula

Forms

Examples

External Links

Source Metadata

Publisher Information