The Fermi-Gas Model

Abstract

The simplest quantum-mechanical systems are free particles. There is no spatial variation in the potential and the relevant Hamiltonian is given merely by the kinetic energy operator. Eigenstates are plane waves labeled by their eigenmomentum k with eigenenergies ε _k = ħ ² k ²/(2m). An interaction-free, continuous many-fermion system is called a Fermi gas. All plane-wave states are occupied up to a certain Fermi energy ε _F , or corresponding Fermi momentum k _F. The density of each plane wave is constant and so is the total density. This, in turn, means that interacting bulk matter when treated at the level of a mean–field approximation (Hartree–Fock or density functional approach, see Chaps. 5 and 6) still has plane waves as eigenstates for the single particle wavefunctions. This allows to use the Fermi gas as an instructive and powerful lowest–order approximation to a great variety of many-fermion systems.