A Real-Valued Formulation of the Time-Dependent Schrödinger Equation via Symmetrical Negative Magnitude Tracks

Abstract:This paper presents a formal derivation of a purely real-valued Time-Dependent Schrödinger Equation, eliminating the historical requirement for the imaginary unit i (where i² = -1) in quantum mechanics. Traditional frameworks necessitate complex-valued fields because the standard legacy number line is structurally asymmetrical, treating the negative domain as a value-sink that induces exponential decay in first-order differential systems. By applying the Identity View of Mirror Magnitude, we establish a mathematically stable, single-dimensional vector space where negative magnitude increases symmetrically away from zero. Under this framework, the sign rules of multi-term operations preserve domain identity, allowing continuous quantum wave oscillations to propagate natively along a purely real track, rendering complex arithmetic patches structurally redundant.