The Schrödinger equation is the foundation of non-relativistic quantum mechanics. It governs the quantum behaviour of everything from atoms to molecules to condensed matter systems. In every physics textbook, it is postulated - motivated by analogy with classical mechanics and the de Broglie wavelength, but not derived from anything more fundamental.
BFUT Paper 19A derives it from the covariant substrate carrier equation F1-cov.
The Derivation Route
The covariant substrate carrier equation F1-cov governs how Spaticle substrate deformations propagate at the relativistic level - it is the full relativistic propagation equation of the substrate medium, derived in Paper 18 from the Spaticle field Lagrangian. In the non-relativistic limit (v ≪ c, low deformation energy), F1-cov reduces to:
The Schrödinger equation is the non-relativistic propagation equation of the Spaticle substrate. It is a limit, not an axiom.
The Coefficient Explained
The coefficient ħ²/2m in the kinetic energy term is not an independent assumption. ħ is derived from condensation geometry in Paper 16. The factor 1/2 is A_model - the dimensionless localisation cost coefficient of the P16 free-energy functional, which equals 1/2 exactly when the ħ derivation is exact. The Schrödinger kinetic term is the condensation localisation cost expressed as a differential operator.
The Dirac Equation
Paper 19A also establishes that the Dirac equation - the relativistic extension of the Schrödinger equation for spin-1/2 particles - follows from F1-cov without taking the non-relativistic limit. The four-component Dirac spinor corresponds to the four degrees of freedom of the condensation's internal circulation state: two spin orientations and two chirality states. The Dirac gamma matrices encode the geometric relationships between these four internal states in the condensation topology.
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