How Natural Origins Achieves the Algebraization of the Schrödinger Equation

This paper develops the algebraization of the Schrodinger equation by reexamining the bottom layer meanings of the wave function, complex phase, kinetic term, potential term, quantum numbers, probability square, interference, uncertainty, and entanglement in modern quantum mechanics. The paper argues that the greatness of the Schrodinger equation lies in its successful compression of a large body of microscopic experimental regularities, while its limitation lies in compressing electron ontology, spatial propagation, path delay, phase relation, boundary action, and material manifestation into one wave function. This compression easily causes the electron itself to be confused with the probability wave. In the Natural Origins framework, the electron is defined as a real closed loop ontology, while the wave function is repositioned as the continuous algorithmic expression of an open ledger. Space unit refresh explains the upper limit of propagation speed, right handed orthogonal refresh explains the complex structure, time element unfolding forms the time potential terrain, the moving unit circle explains the square structure of the kinetic term, orbital volume hierarchy explains principal quantum numbers and energy levels, and elemental cell restoration work explains the material manifestation source of the probability square. In this way, the Schrodinger equation is no longer understood as a mysterious equation of electron probability wave motion. It is reduced to a continuous algorithmic compression describing how, after a complete electron enters a time potential terrain, the open ledger is refreshed through space units, constrained by time potential, reissued through boundaries, and finally squared into manifestation at the elemental cell endpoint. The paper further states that interference is not the splitting of the electron ontology, but the spatial settlement pattern formed after an open ledger is reissued by boundary elemental cells. Uncertainty is not the absence of a definite state of the electron ontology, but the minimum exchange residual between path process ledger and material manifestation ledger. Entanglement is not remote notification, but a double endpoint shared relational ledger opened from the same source event. The whole paper finally forms a unified main line: space units are responsible for propagation, right handed refresh is responsible for orthogonality, time elements are responsible for potential terrain, open ledgers are responsible for unsealed relations, boundaries are responsible for reissuance, and elemental cells are responsible for final manifestation. The Schrodinger equation is thereby transformed from a quantum mystical image into a clear algebraic ontological chain.