Exact Analytical Solutions to the Schrödinger Equation via Sexagesimal Harmonic Mathematics (MAS) and the Balance of Maat Framework
Authors/Creators
Description
Statement of Ethical Principles and Conceptual Purpose
This work is formulated under the foundational ethical principle of the Balance of Maat—a commitment to universal equilibrium, truth, geometric order, and the systematic neutralization of mathematical and physical chaos (*Isfet*). The primary objective of the Sexagesimal Harmonic Mathematics (MAS) framework and the Sexagesimal Harmony Algorithm (AAS) is to advance the unification of scientific knowledge through strict analytical rigor, structural stability, and constructive harmonic modeling. This theoretical framework is explicitly dedicated to the peaceful advancement of mathematical physics, the elimination of non-physical singularities, and the cultivation of an integrative paradigm that restores symmetry and balance to our understanding of quantum phenomena. Researchers and readers are invited to engage with this material in the spirit of intellectual integrity, harmony, and the collective progress of humanity.
Overview
By mapping the quantum Hilbert space H onto a discrete-continuous sexagesimal modular lattice defined over base-60 residue rings Z_60, this paper delivers exact analytical solutions to the time-independent Schrödinger equation. Differential operators, potential landscapes, and spatial Laplacians are reformulated using sexagesimal angular metrics θ _60, successfully regularizing central Coulombic singularities into finite, topologically stable harmonic cores. The accompanying proofs establish that probability flux conservation ∇ \cdot fJ = 0) and operator Hermiticity are direct geometric expressions of universal balance, offering complete closed-form wavefunctions and exact energy spectra for both the Sexagesimal Harmonic Oscillator and the Radial Hydrogen Atom.
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