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Fermi Energy for Non-Interacting Fermions

The Fermi energy is a concept in quantum mechanics usually referring to the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature.

The Fermi energy is proportional to the two-thirds power of the ratio between the number density of the gas and 1 plus twice the particle spin. It is also inversely proportional to the mass of the individual particles.

Formula

QuantityVariable[Subscript["E", "f"], "Energy"] == (Quantity[(3^(2/3)*Pi^(4/3))/2^(1/3), "ReducedPlanckConstant"^2]*(QuantityVariable["n", "InverseVolume"]/(1 + 2*QuantityVariable["s", "Unitless"]))^(2/3))/QuantityVariable["m", "Mass"]

symbol description physical quantity
Ef fermion energy "Energy"
m mass "Mass"
n fermion number density "InverseVolume"
s particle spin "Unitless"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Fermi Energy for Non-Interacting Fermions"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ ResourceObject["Fermi Energy for Non-Interacting Fermions"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Fermi Energy for Non-Interacting Fermions"], {QuantityVariable[ "m","Mass"] -> Quantity[1, "ElectronMass"]}]
Out[3]=

Source Metadata

  • Creator:
  • Date: 1926

Publisher Information