Compton wavelength

The Compton wavelength is a quantum mechanical property of a particle. It was introduced by Arthur Compton in his explanation of the scattering of photons by electrons (a process known as Compton scattering). The Compton wavelength of a particle is equal to the wavelength of a photon whose energy is the same as the mass (see mass–energy equivalence) of that particle. The standard Compton wavelength, λ, of a particle is given by where h is the Planck constant, m is the particle's mass, and c is the speed of light. The significance of this formula is shown in the derivation of the Compton shift formula. The CODATA 2014 value for the Compton wavelength of the electron is 2.4263102367(11)×10−12 m. Other particles have different Compton wavelengths. When the Compton wavelength is divided by 2π, one obtains the 'reduced' Compton wavelength ƛ (barred lambda), i.e. the Compton wavelength for 1 radian instead of 2π radians: where ħ is the 'reduced' Planck constant. The inverse reduced Compton wavelength is a natural representation for mass on the quantum scale, and as such, it appears in many of the fundamental equations of quantum mechanics. The reduced Compton wavelength appears in the relativistic Klein–Gordon equation for a free particle: It appears in the Dirac equation (the following is an explicitly covariant form employing the Einstein summation convention):