ATOMS AS VIBRATING RINGS: A GEOMETRIC INTERPRETATION OF QUANTUM MECHANICS

This paper presents a novel geometric interpretation of quantum mechanics: the Vibrating Ring Theory. By modeling electrons as vibrating rings on atomic nuclei, we provide intuitive geometric meanings for quantum numbers and demonstrate the theory's predictive power for atomic properties. The theory achieves perfect prediction for hydrogen (0.2% radius error, 0.0% ionization energy error), 10.9% average error for atomic radii of period 1-2 elements, and maintains full mathematical consistency. The periodicity of spin-1/2 particles emerges naturally from the ring vibration model. Our work bridges classical vibration concepts with quantum phenomena, offering valuable pedagogical insights.Keywords: Quantum Mechanics, Geometric Interpretation, Vibrating Rings, Spin Periodicity, Atomic Properties