Electromagnetic theory relativistic Schrodinger equation. Its solution and the scattering cross section for superluminal particles

摘要

From the author's previous paper [Phys. Essays 11, 77 (1998)] on time dilation by electromagnetic (EM) theory, the relativistic kinetic energy written in Hamiltonian form allows the derivation of Schrodinger's equation without speed of light limitations on its wavefunction solutions. The wavefunction representing a "one-dimensional particle" may move at subluminal (hypophotic), luminal (photic), or superluminal (hyperphotic) velocities. The EM relativistic Schrodinger equation was solved for the far-field form of the wave function which had a characteristic "teardrop" shape. This shape is apparently a characteristic of a superluminal particle. The velocity expectation value of the wavefunction was also calculated. It is proposed that the meson exchanged radially between the neutron and proton in a deuteron and having a rest mass of about 470 MeV may be a superluminal particle upon its ejection from the deuteron nucleus. It was found that its velocity expectation value was about 1.233c upon its ejection from the deuteron nucleus. The expectation value of its length was found to be about 0.7164 fm. Using the Born approximation and the Green's function derived by Fourier transform, the scattering cross section was calculated when the scatterer in the Schrodinger equation was a spherically symmetric screened Coulomb potential. The classic Rutherford scattering cross section of alpha particles scattered from a gold foil was compared to the scattering cross section for the scattering of superluminal particles. The scattering of superluminal particles had a very much smaller intensity than the scattering of alpha particles. [References: 15]