Thomas–Fermi model

The Thomas–Fermi (TF) model, named after <a href="/facts/Llewellyn_Thomas/cAzzHNCg">Llewellyn Thomas</a> and <a href="/facts/Enrico_Fermi/cmYcY15H">Enrico Fermi</a>, is a <a href="/facts/Quantum_mechanical/BRc3Mzgr">quantum mechanical</a> theory for the <a href="/facts/Electronic_structure/RuHwQWfp">electronic structure</a> of <a href="/facts/Many-body/n2rIxgwv">many-body</a> systems developed <a href="/facts/Semiclassical_physics/8v1CG3RP">semiclassically</a> shortly after the introduction of the <a href="/facts/Schr%25C3%25B6dinger_equation/3csgSIWF">Schrödinger equation</a>. It stands separate from <a href="/facts/Wave_function/KgM5ykjY">wave function</a> theory as being formulated in terms of the <a href="/facts/Electronic_density/L5yDsk6j">electronic density</a> alone and as such is viewed as a precursor to modern <a href="/facts/Density_functional_theory/wwz4Gqdg">density functional theory</a>. The Thomas–Fermi model is correct only in the limit of an infinite <a href="/facts/Nuclear_charge/FFpQ0ubY">nuclear charge</a>. Using the approximation for realistic systems yields poor quantitative predictions, even failing to reproduce some general features of the density such as shell structure in atoms and <a href="/facts/Friedel_oscillation/QyqrshEs">Friedel oscillations</a> in solids. It has, however, found modern applications in many fields through the ability to extract qualitative trends analytically and with the ease at which the model can be solved. The kinetic energy expression of Thomas–Fermi theory is also used as a component in more sophisticated density approximation to the kinetic energy within modern <a href="/facts/Orbital-free_density_functional_theory/vk9kPDol">orbital-free density functional theory</a>.
Working independently, Thomas and Fermi used this model in 1927 to approximate the distribution of electrons in an atom. Although electrons are distributed nonuniformly in an atom, the approximation was made that in each small volume element ΔV (i.e. locally), the electrons are distributed uniformly. The electron density 
 
 
 
 n
 (
 
 r
 
 )
 
 
 {\displaystyle n(\mathbf {r} )}
 
 can still vary from one volume element to the next.

Thomas–Fermi model open-in-new

Thomas–Fermi model