Quantum Mechanics: Internal Motion in Theory and Experiment

Abstract

Dispersion dynamics applies wave-particle duality, together with Maxwell’s electromagnetism, and with quantization E = hν = ħ ω (symbol definitions in footnote) and p = h/λ = ħ k , to special relativity E 2 = p 2 c 2 + m 2 c 4 . Calculations on a wave-packet, that is symmetric about the normal distribution, are partly conservative and partly responsive. The complex electron wave function is chiefly modelled on the real wave function of an electromagnetic photon; while the former concept of a “point particle” is downgraded to mathematical abstraction. The computations yield conclusions for phase and group velocities, v p ⋅ v g = c 2 with v p ≥ c because v g ≤ c , as in relativity. The condition on the phase velocity is most noticeable when p ≪ mc . Further consequences in dispersion dynamics are: derivations for ν and λ that are consistently established by one hundred years of experience in electron microscopy and particle accelerators. Values for v p = ν λ = ω/k are therefore systematically verified by the products of known multiplicands or divisions by known divisors, even if v p is not independently measured. These consequences are significant in reduction of the wave-packet by resonant response during interactions between photons and electrons, for example, or between particles and particles. Thus the logic of mathematical quantum mechanics is distinguished from experiential physics that is continuous in time, and consistent with uncertainty principles. [Footnote: symbol E = energy; h = Planck’s constant; ν = frequency; ω = angular momentum; p = momentum; λ = wavelength; k = wave vector; c = speed of light; m = particle rest mass; v p = phase velocity; v g = group velocity].