Fermi_energy

plasmapy.formulary.quantum.Fermi_energy(n_e: Unit(‘1 / m3’))

Calculate the kinetic energy in a degenerate electron gas.

Aliases: Ef_

Parameters

n_e (Quantity) – Electron number density.

Returns

energy_F – The Fermi energy in joules.

Return type

Quantity

Raises

• TypeError – If argument is not a Quantity.

• UnitConversionError – If argument is in incorrect units.

• ValueError – If argument contains invalid values.

Warns

UnitsWarning – If units are not provided, SI units are assumed.

Notes

The Fermi energy is the kinetic energy in a degenerate electron gas and is given by

\[E_F = \frac{π^2 ℏ^2}{2 m_e} \left( \frac{3 n_e}{π} \right)^{2/3}\]

This quantity is often used in place of thermal energy for analysis of cold, dense plasmas (e.g. warm dense matter, condensed matter).

See also

Thomas_Fermi_length

Example

>>> from astropy import units as u
>>> Fermi_energy(1e23 * u.cm**-3)
<Quantity 1.2586761e-18 J>