Volume 14: Pages 203-207, 2001 (doi:http://dx.doi.org/10.4006/1.3025484)
Particles at Cutoffs in the Electromagnetic Spectrum
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A finite‐difference formulation of Maxwell's equations in free space leads to electromagnetic wave propagation governed by the nonlinear dispersion relationship ω = ωc|sin(kλc)|, where ωc = c/λc, c is the speed of light, and λc is the Compton wavelength. This corresponds to the classical dispersion relationship ω = kc in the limit of frequencies far below cutoffs in the electromagnetic spectrum at ωc = mc2/ħ. Since the group velocity is νg ≡ dω/dk = c|cos(kλc)|, the dispersion relationship can also be expressed in terms of observables νg and c as ω = ωc(1 − (νg/c)2)1/2. In addition, it is shown that dispersive wave‐packets near cutoff correspond to the Schrödinger equation for a free particle.
Keywords: electromagnetic spectrum, dispersion, Compton wavelength, cutoff frequency, Lorentz transformation, wave‐packets, Schrödinger equation, particles
Received: May 13, 1999; Published online: December 15, 2008