Friedel oscillations, named after French physicist Jacques Friedel, arise from localized perturbations in a metallic or semiconductor system caused by a defect in the Fermi gas or Fermi liquid. Friedel oscillations are a quantum mechanical analog to electric charge screening of charged species in a pool of ions. Whereas electrical charge screening utilizes a point entity treatment to describe the make-up of the ion pool, Friedel oscillations describing fermions in a Fermi fluid or Fermi gas require a quasi-particle or a scattering treatment. Such oscillations depict a characteristic exponential decay in the fermionic density near the perturbation followed by an ongoing sinusoidal decay resembling sinc function. In 2020, magnetic Friedel oscillations were observed on a metal surface. One-dimensional electron gas As a simple model, consider one-dimensional electron gas in a half-space . The electrons do not penetrate into the half-space , so that the boundary condition for the electron wave function is . The oscillating wave functions that satisfy this condition are , where is the electron wave vector, and is the length of the one-dimensional box (we use the 'box" normalization here). We consider degenerate electron gas, so that the electrons fill states with energies less than the Fermi energy . Then, the electron density is calculated as , where summation is taken over all wave vectors less than the Fermi wave vector , the factor 2 accounts for the spin degeneracy. By transforming the sum over into the integral we obtain . We see that the boundary perturbs the electron density leading to its spatial oscillations with the period near the boundary. These oscillations decay into the bulk with the decay length also given by . At the electron density equals to the unperturbed density of the one-dimensional electron gas . Scattering description The electrons that move through a metal or semiconductor behave like free electrons of a Fermi gas with a plane wave-like wave function, that is . Electrons in a metal behave differently than particles in a normal gas because electrons are fermions and they obey Fermi–Dirac statistics. This behaviour means that every k-state in the gas can only be occupied by two electrons with opposite spin. The occupied states fill a sphere in the band structure k-space, up to a fixed energy level, the so-called Fermi energy. The radius of the sphere in k-space, kF, is called the Fermi wave vector. If there is a