The Eigenvalue Spectrum of Atomic Structure: Physical Origins of Chemical Bonds and the Periodic Table
Year: 2026
Type: preprint
Abstract: The statistical interpretation of the wave function in quantum mechanics has achieved great mathematical success, but its popular presentation has led to a widespread intuitive misunderstanding — electrons are imagined as diffuse probability clouds surrounding the nucleus, rather than as stable entities confined to specific geometric boundaries. Starting from two geometric axioms, this paper establishes a geometric dynamics framework (GDUT) based on the evolution of three-dimensional spatial curvature, reducing the electron to a stable soliton solution of the modified Ricci flow in a spherically symmetric potential well. The derivation shows that electron shell radii obey an integer eigenvalue spectrum of n^2, the number of electrons in a given shell is constrained by spherical surface density, and a filled shell corresponds to a geometrically rigid state. This framework provides a unified geometric explanation for atomic structure and chemical bonds that requires no externally imposed quantum assumptions, and its predictions are in excellent numerical agreement with experimental data.
Author: Ma, Ning
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7210279900
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