Fermi_energy¶
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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: Raises: TypeError
– If argument is not aQuantity
.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
Example
>>> from astropy import units as u >>> Fermi_energy(1e23 * u.cm**-3) <Quantity 1.2586761e-18 J>