Reconsidering the Completed Form of the Wave Equation --- Phase Evolution, Non-Zero Energy, and a Reinterpretation of Probability ---

This paper revisits the wave equation originally suggested by Einstein and examines the possibility that it constitutes a complete description of particle motion without requiring a fundamental probabilistic interpretation. It proposes that intrinsic physical fluctuations of particles can account for phenomena typically attributed to quantization and superposition. The double-slit experiment is reinterpreted from this perspective, suggesting that interference patterns may arise naturally from particle fluctuations interacting with boundary conditions. This work offers a conceptual reevaluation of wave–particle duality and discusses whether quantization should be regarded as a necessary fundamental principle or as a posteriori interpretation.