A Local-Ether Wave Equation Unifying
Quantum Mechanics, Electromagnetics, and Gravitation
Chapter 4 Modifications of Schrodinger's Equation
A wave equation incorporating a natural frequency and the electric scalar potential is presented, which is supposed to govern the matter wave of a charged particle, which in turn is supposed to follow the local-ether propagation model. From the local-ether wave equation, the electrostatic force together with the inertial mass is derived. As a consequence, it is found that the inertial mass of a charged particle originates from the temporal variation of the associated matter wave. Further, the wave equation is refined by connecting the scalar potential with the augmentation operator which is associated with the momentum operator and the velocity of the source particles. From this local-ether wave equation, a first-order time evolution equation is derived, which in turn leads to the electromagnetic force law based on the augmented potentials proposed in Chapter 2. Under some ordinary conditions, this law reduces to the modified Lorentz force law. The evolution equation then represents modifications of Schrodinger's equation complying with Galilean transformations and the local-ether propagation model. The fundamental modification is that the position vector and the time derivative are referred specifically to the local-ether frame. Furthermore, the role of the vector potential in Schrodinger's equation is replaced by the augmentation operator connected with the scalar potential. The evolution equation looks quite different from Schrodinger's equation. However, under some ordinary conditions, it is shown that these two equations become substantially identical.
This Chapter is based on:
C.C. Su, "A local-ether wave equation and the consequent electromagnetic force law," J. Electromagnetic Waves Applicat., vol. 16, pp. 1275-1290, Sept. 2002.
C.C. Su, "Modifications of Schrodinger's equation complying with the effect of earth's rotation on quantum energy in atoms and with the electromagnetic force," http://arXiv.org/physics/0208083.
C.C. Su, "A local-ether wave equation and the Galilean-invariant electromagnetic force law," in IEEE Antennas Propagat. Soc. Int. Symp. Dig., vol. 1, pp. 216-219. July 2001.
C.C. Su, "Modifications of Schrodinger's equation invariant under Galilean transformations," in Bull. Am. Phys. Soc., vol. 46, no. 1, p. 1144, Mar. 2001.
Full texts of major papers contributing to this Chapter (in PDF)
(1) Wave equation and force law,