Fermi Energy

The Fermi energy is a concept in quantum mechanics referring to the energy of the highest occupied quantum state in a system of fermions atabsolute zero temperature. This article requires a basic knowledge of quantum mechanics. Encyclopedia > Fermi energy The Fermi energy is a concept in quantum mechanics referring to the energy of the highest occupied quantum state in a system of fermions atabsolute zero temperature. This article requires a basic knowledge of quantum mechanics. Contents 1 Introduction 1.1 Context 1.2 Advanced Context 2 Illustration of the concept for a one dimensional square well 3 The three dimensional case 4 Typical fermi energies 4.1 White dwarfs 4.2 Nucleus 5 Fermi level 6 Quantum mechanics 7 Free electron gas 8 See also 9 References Introduction Context In quantum mechanics, a group of particles known as fermions (for example, electrons, protons and neutronsare fermions) obey the Pauli exclusion principle. This principle states that two identical fermions can not be in the same quantum state. The states are labeled by a set of quantum numbers. In a system containing many fermions (like electrons in a metal) each fermion will have a different set of quantum numbers. To determine the lowest energy a system of fermions can have, we first group the states in sets with equal energy and order these sets by increasing energy. Starting with an empty system, we then add particles one at a time, consecutively filling up the unoccupied quantum states with lowest-energy. When all the particles have been put in, the Fermi energy is the energy of the highest occupied state. What this means is that even if we have extracted all possible energy from a metal by cooling it down to near absolute zero temperature (0 Kelvin), the electrons in the metal are still moving around, the fastest ones would be moving at a velocity that corresponds to a kinetic energy equal to the Fermi energy. This is the Fermi velocity. The Fermi energy is one of the important concepts of condensed matter physics. It is used, for example, to describe metals, insulators, andsemiconductors. It is a very important quantity in the physics of superconductors, in the physics of quantum liquids like low temperature helium (both normal 3He and superfluid 4He), and it is quite important to nuclear physics and to understand the stability of white dwarf stars against gravitational collapse. Advanced Context The Fermi energy (EF) of a system of non-interacting fermions is the increase in the ground state energy when exactly one particle is added to the system. It can also be interpreted as the maximum energy of an individual fermion in this ground state. The chemical potential at zero temperature is equal to the Fermi energy.