Schr¨odinger Equation from Variational Stability in Non-Inertial Dynamics

This preprint presents a derivation of the Schrödinger equation from a classical variational principle that includes higher-order derivatives and stochastic non-inertial dynamics. Planck’s constant is interpreted as a parameter of residual inertial fluctuations. The approach reproduces quantum features such as interference and hydrogen energy levels without postulating quantum axioms. This version includes updated analytical and numerical calculations for energy levels, a discussion of stability criteria, and a quantitative model for electron diffraction. The energy-power balance formulation for stationary states is newly integrated. This work is shared to establish conceptual priority. A peer-reviewed submission based on this work is in preparation.