A local-ether wave equation and the Galilean-invariant electromagnetic force law

In a Galilean theory recently developed, the Lorentz force law has been modified in such a way that the electromagnetic force is invariant when observed in different inertial frames, as expected intuitively. In this investigation, based on the local-ether model of wave propagation, a Galilean-invariant wave equation is proposed. This wave equation incorporates a natural frequency and the electric scalar potential. A unique feature is that this potential connects to the augmentation operator which in turn is associated with the momentum operator and the velocity of the source particle. From this local-ether wave equation, a first-order time evolution equation is derived, which presents Galilean modifications of Schrodinger´s equation. This modified equation in turn leads to the Galilean-invariant electromagnetic force law given in terms of the augmented potentials.