structural:summarization, linguistic:translation
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.
In a Fermi gas, the lowest occupied state is taken to have zero kinetic energy, whereas in a metal, the lowest occupied state is typically taken to mean the bottom of the conduction band. The term "Fermi energy" is often used to refer to a different yet closely related concept, the Fermi level.
There are a few key differences between the Fermi level and Fermi energy, at least as they are used in this article: The Fermi energy is only defined at absolute zero, while the Fermi level is defined for any temperature.
The Fermi energy is an energy difference, whereas the Fermi level is a total energy level including kinetic energy and potential energy.
The Fermi energy can only be defined for non-interacting fermions, whereas the Fermi level remains well defined even in complex interacting systems, at thermodynamic equilibrium. Since the Fermi level in a metal at absolute zero is the energy of the highest occupied single particle state,
then the Fermi energy in a metal is the energy difference between the Fermi level and lowest occupied single-particle state, at zero-temperature.