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 orbital-free density functional theory. 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. 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 Friedel oscillations in solids. The former condition corresponds, in a real experiment, to keeping the metal/fluid in electrical contact with a fixed potential difference with ground.
The TF model is correct only in the limit of an infinite nuclear charge. In the ThomasFermi approximation, 4 named after Llewellyn Thomas and Enrico Fermi, the system is maintained at a constant electron chemical potential (Fermi level) and at low temperature. It stands separate from wave function theory as being formulated in terms of the electronic density alone and as such is viewed as a precursor to modern density functional theory. THOMAS - FERMI MOD£L The crude models of the preceding Chapter taught us that it may be useful to treat the electrons in an atom (or ion) as if they were moving independently in an effective potential.
The Thomas–Fermi (TF) model, named after Llewellyn Thomas and Enrico Fermi, is a quantum mechanical theory for the electronic structure of many-body systems developed semiclassically shortly after the introduction of the Schrödinger equation.