freeelectron

A free electron is an electron that is not bound to an atom, molecule, or crystal lattice. In vacuum, it behaves as a quantum particle with a well-defined momentum and energy, described by its wavefunction. The simplest description uses nonrelativistic quantum mechanics, in which the stationary states are plane waves and the energy-momentum relation is E = p^2/(2m), where p is the momentum and m is the electron mass. Relativistically, the energy satisfies E^2 = p^2 c^2 + m^2 c^4, as given by the Dirac equation, which also incorporates the electron’s spin of 1/2.

In practice, free electrons are idealizations. They experience no binding forces in the absence of external fields, but external electromagnetic fields can influence their motion. In many physical contexts, such as plasmas or high-energy processes, electrons can be treated as nearly free over short ranges or times, with corrections from interactions with other charges, fields, and radiation.

In solids, the concept is approximated by the free electron gas model, where conduction electrons move through a uniform positive background. This model yields a simple parabolic energy-band structure near the Fermi level and helps explain metallic conductivity and electronic heat capacity. Real materials show deviations due to lattice potentials, electron–electron interactions, and band structure, but the free electron picture remains a foundational reference point.

Free electrons are central to electronics, plasma physics, and many areas of physics and engineering, providing a baseline for understanding more complex bound and interacting systems.