Modifications of Schr\"{o}dinger's Equation Complying with the Effect of Earth's Rotation on Quantum Energy in Atoms and with the Electromagnetic Force

Abstract

Recently, we have presented a local-ether wave equation incorporating a nature frequency and the electric scalar potential, from which the speed-dependences in the angular frequency and wavelength of matter wave, in the mass of particle, and in the energy of quantum states are derived. These relations look like the postulates of de Broglie and the Lorentz mass-variation law, except that the particle speed is referred specifically to a geocentric inertial frame and hence incorporates earth's rotation for earthbound particles. Further, the wave equation is extended by connecting the scalar potential to the augmentation operator which is associated with a velocity difference between involved particles. Then the electromagnetic force law is derived, which under some ordinary conditions reduces to the modified Lorentz force law. In this investigation, the interaction of atoms with electromagnetic radiation is explored. Then it is shown that the time evolution equation derived from the wave equation is substantially identical to Schr\"{o}dinger's equation incorporating the vector potential, if the latter is observed in the atom frame and if the source generating the vector potential is electrically neutralized, as in common practice.