# Fermi_energy¶

plasmapy.physics.quantum.Fermi_energy(n_e)

Calculate the kinetic energy in a degenerate electron gas.

Parameters

n_e (Quantity) – Electron number density.

Returns

energy_F – The Fermi energy in Joules.

Return type

Quantity

Raises
Warns

~astropy.units.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

$E_F = \frac{\pi^2 \hbar^2}{2 m_{e}} \left( \frac{3 n_{e}}{\pi} \right )^{2/3}$

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

Example

>>> from astropy import units as u
>>> Fermi_energy(1e23 * u.cm**-3)
<Quantity 1.25867611e-18 J>