Application of Fractal Wavefunctions in Quantum Mechanics: A Framework for Wavefunction Geometrization, Decoherence, and Time Irreversibility

changzheng zhou, ZIQING zhou

Published Feb 19, 2025• 0 citations

Abstract

This paper introduces a unified fractal wavefunction model by incorporatinga dynamic fractal dimension Df (t), providing novel explanations for wavefunc?tion geometrization, decoherence, and time irreversibility in quantum mechanics.By reinterpreting the physical essence of the wavefunction from the perspectiveof fractal geometry, we propose a fractal Schr¨odinger equation and demonstratethe extensive applicability of fractal wavefunctions in quantum systems throughexperimental validation and numerical simulations. The primary innovations in?clude the introduction of dynamic fractal dimensions, mathematical modeling offractal wavefunctions, and a geometric interpretation of decoherence and time irre?versibility. With supplementary theoretical foundations, experimental designs, andnumerical analyses, this work enhances the academic rigor and credibility of theproposed model.

DOI: 10.31219/osf.io/7xdce_v1

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