A gravitational orbit simulation program was used to classically map orbital transition in the H atom. The electron in transition mapped a hyperbolic spiral path. Notably at intervals the spiral angles converged to give integer radius of the form n^2r (360°=4r, 360+120°=9r, 360+180°=16r, 360+216°=25r ... 720°=∞ ...). The period between these radius gives the transition frequencies. As these transitions are a function of pi, could quantization in the atom have geometric origins?

The simulation source codes are available here: https://codingthecosmos.com/orbitals.html

Article:

  • Preprint Simulating gravitational and atomic orbits via rotating part...

Summary:

https://en.wikiversity.org/wiki/Quantum_gravity_(Planck)

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