Closed Surface Quantization: Discrete Energy States and Automatic Hierarchy Generation

This study introduces a topological model of quantization in which electrons are represented not as point particles but as quantized surface elements governed by discrete phase conditions. A closed surface forms only when the phase Φ spans from 000 to 2πn22\pi n^22πn2, leading to allowable electron counts N=2n^2for each quantized surface layer. The wave nature of these surfaces is expressed via complex phase functions eiΦe^{i\Phi}, whose real components cos⁡(2πk/n) correspond to physically stable momentum-energy distributions. This framework inherently produces discrete energy levels and a self-generating hierarchy of states. The model bridges geometric surface theory, number theory, and quantum structure, providing an alternative to conventional probabilistic interpretations of quantum mechanics.

Author: Konno Tetsuo(今野哲夫)

https://orcid.org/0009-0002-1842-7865 tetsuo@mug.biglobe.ne.jp