Rethink quantization of atomic orbitals as emerging from dynamics: Reproduction of Dirac physics without spin

Exploring the possibility that quantization of electronic orbitals may emerge from rapid intra-atomic dynamics beyond current experimental capability, we reconstruct the quantization condition based on the electronic planner motion. In hydrogenic systems, this automatically leads to half-integer orbital angular momenta with characteristics nearly identical to those of the Dirac equation, without introducing spin or special relativity.This result naturally explains the lack of Stern-Gerlach experimental splitting of electrons and suggests a possible microscopic interpretation of the spin as an effective patch-up for the unaccounted orbital angular momentum, rather than an intrinsic self-rotation of electrons.More importantly, this study paves the way for further investigation on possible dynamical emergence of quantization in quantum mechanics.