Fermi_energy

plasmapy.formulary.quantum.Fermi_energy(n_e: Unit("1 / m3")) -> Unit("J")

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:

~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).

See also

Thomas_Fermi_length()

Example

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