Fermimomentum

Fermimomentum refers to the maximum momentum that a fermion can possess within a degenerate Fermi gas at absolute zero temperature. In a Fermi gas, particles are governed by the Pauli exclusion principle, meaning no two identical fermions can occupy the same quantum state. As the temperature approaches absolute zero, these fermions fill up available energy levels from the lowest up to a certain maximum energy level, known as the Fermi energy. The momentum associated with this Fermi energy is the fermimomentum.

Mathematically, the fermimomentum ($p_F$) is related to the Fermi energy ($E_F$) by the non-relativistic relation $E_F = p_F^2 / (2m)$, where $m$ is the mass of the fermion. It can also be expressed in terms of the particle number density ($n$) of the system. For a three-dimensional gas of spin-1/2 fermions, the fermimomentum is given by $p_F = \hbar (3\pi^2 n)^{1/3}$, where $\hbar$ is the reduced Planck constant. This relationship highlights that a higher particle density leads to a higher fermimomentum.

The concept of fermimomentum is crucial in understanding the properties of various physical systems, including white dwarf stars, neutron stars, and the behavior of electrons in metals. In these systems, at low temperatures, the particles behave as a degenerate Fermi gas, and their properties are largely determined by the fermimomentum and Fermi energy. It dictates the pressure, compressibility, and thermal conductivity of these materials.