Relationship Between The Reduced and Non-reduced Compton Wavelength
The reduced Compton wavelength is a natural representation for mass on the quantum scale. Equations that pertain to mass in the form of mass, like Klein-Gordon and Schrödinger's, use the reduced Compton wavelength. The non-reduced Compton wavelength is a natural representation for mass that has been converted into energy. Equations that pertain to the conversion of mass into energy, or to the wavelengths of photons interacting with mass, use the non-reduced Compton wavelength.
A particle of rest mass m has a rest energy of E = mc2. The non-reduced Compton wavelength for this particle is the wavelength of a photon of the same energy. For photons of frequency f, energy is given by
which yields the non-reduced Compton wavelength formula if solved for λ.
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