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 equivalent to the wavelength of a photon whose energy is the same as the rest-mass energy of the particle.

The Compton wavelength, λ, of a particle is given by

<math> lambda = frac </math>

where h is the Planck constant, m is the particle's rest 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 2006 value for the Compton wavelength of the electron is .CODATA 2006 value for for the electron from NIST Other particles have different Compton wavelengths.

Significance

Reduced Compton wavelength

When the Compton wavelength is divided by <math></math>, one obtains a smaller or “reduced” Compton wavelength:

<math> frac = frac </math>

The 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:

<math> mathbf^2psi-fracfracpsi = left(frac right)^2 psi </math>

It appears in the Dirac equation (the following is an explicitly covariant form...
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