Deriving the Schrödinger Equation from Source-Free Maxwell Dynamics

Maxwell's equations for electromagnetism in source-free vacuum predict discrete energies when an electromagnetic field forms a self-confined toroidal standing pattern. For any component $F(\mathbf{r},t)$ of the electromagnetic fields $\mathbf{E}, \mathbf{B}$, we isolate the forward-time spectral part, keep all derivative terms exactly, and obtain —within a rigorously bounded, bandwidth-squared remainder— the Schrödinger equation. Planck's constant and the inertial mass thus emerge not as fundamental constants, but as geometric properties of the fundamental toroidal mode ($E_{11}, \omega_{11}$).