On the Thomas–Fermi model at the Planck scale

Many quantum gravity theories predict a minimal length of the order of the Planck length. In this letter, the Thomas–Fermi model is reformulated by taking into account such a prescription. A generalized Thomas–Fermi equation is derived, that reduces to the usual one in the absence of a minimal length. As an application, the model is used to study the dielectric screening process. Estimations of the Fermi length are given for star interior.

Thomas–Fermi model Generalized uncertainty principle Minimal length uncertainty Screening process