Exact Analytical Solutions to the Schrödinger Equation via Sexagesimal Harmonic Mathematics (MAS) and the Balance of Maat Framework

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. SHM: Application to Millennium Problems, Conjectures, and Theoretical Physics The Sexagesimal Cosmological Model (SCM): A Unified Theory of Fundamental Forces, Singularity Stability, and the López Harmonic Constant. 2026-04-29 | Preprint https://doi.org/10.5281/zenodo.23438041 On the Geometric Resonances of the Riemann Zeta Function A Sexagesimal Harmony Approach 2026-05-10 | Preprint DOI: 10.5281/ZENODO.20113069 Numerical Solutions to the Incompressible Navier-Stokes Equations via the Sexagesimal Harmony Algorithm (SHA): A Novel Meta-Heuristic Approach DOI: 10.5281/ZENODO.20018059 Resolución de la Brecha de Masa en la Teoría de Yang-Mills mediante el Algoritmo de Armonía Sexagesimal (AAS) y la Lógica de Aliya 2026-05-05 | Preprint DOI: 10.5281/ZENODO.20040782 Solución a la conjetura de Birch y Swinnerton Dyer DOI: 10.5281/ZENODO.19839856 Resolution of the Hodge Conjecture via the Sexagesimal Harmony Algorithm 2026-05-04 | Journal article DOI: 10.5281/ZENODO.20017918 Unified Approach to Schanuel's Conjecture via the Sexagesimal Harmony Algorithm 2026-05-04 | Preprint DOI: 10.5281/ZENODO.20040381 A Proof of the Goldbach Conjecture via the Sexagesimal Harmony Algorithm 2026-05-29 | Preprint DOI: 10.5281/ZENODO.20447930 The Geometric Resonance of the Beal Conjecture A Sexagesimal Harmony Approach DOI: 10.5281/ZENODO.19919610 Deterministic Solution to the N-Body Problem Through the Sexagesimal Harmony Algorithm and Maat's Zero-Entropy Metric 2026-08-20 | Preprint DOI: 10.5281/ZENODO.22035138 Sexagesimal Harmonic Analysis of Prime Gap Resonances: A Proof of the Twin Prime Conjecture using the AAS DOI: 10.5281/ZENODO.23063192 Communitas scientifica, avemus aevum sexagesimale!