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

@misc{miranda2026exact,
  title = {{Exact Analytical Solutions to the Schrödinger Equation via Sexagesimal Harmonic Mathematics (MAS) and the Balance of Maat Framework}},
  author = {Jorge Alexander Lopez Miranda},
  howpublished = {Zenodo},
  year = {2026},
  month = oct,
  doi = {10.5281/zenodo.23475723},
  url = {https://zenodo.org/records/23475723},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Exact Analytical Solutions to the Schrödinger Equation via Sexagesimal Harmonic Mathematics (MAS) and the Balance of Maat Framework
AU  - Jorge Alexander Lopez Miranda
PY  - 2026
DA  - 2026/10/19
PB  - Zenodo
DO  - 10.5281/zenodo.23475723
UR  - https://zenodo.org/records/23475723
AB  - 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!
ER  -