freefermion

A free fermion is a quantum mechanical particle that experiences no interactions with other particles or external fields. In essence, it behaves as if it were isolated, with its motion solely determined by the principles of quantum mechanics. The term "fermion" refers to particles that obey Fermi-Dirac statistics, which are characterized by the Pauli exclusion principle. This principle states that no two identical fermions can occupy the same quantum state simultaneously.

The concept of free fermions is fundamental in many areas of physics, particularly in condensed matter physics and quantum field theory. For instance, in the study of metals, the valence electrons are often approximated as free fermions. This simplification allows physicists to understand the collective behavior of a large number of electrons, such as their electrical conductivity, without needing to account for the complex interactions between them. Similarly, in nuclear physics, nucleons (protons and neutrons) can sometimes be treated as quasi-free particles within the nucleus.

The mathematical description of a free fermion is relatively straightforward. Its behavior is governed by the Schrödinger equation, but without any potential energy terms other than those that might define the boundaries of its confinement, if any. The solutions to the Schrödinger equation for free fermions are typically plane waves, representing particles that are delocalized throughout space. When these free fermions are confined to a finite volume, their energy levels become quantized, a phenomenon that underpins many solid-state phenomena. Despite the idealized nature of the "free" assumption, it provides a crucial starting point for understanding more complex, interacting systems.