Arnaud Lazarus (Institut ∂'Alembert). Modulation-Induced Quantization in Fundamentally Unstable Systems: Application to Bohr's Atomic Model.

In this talk, we numerically investigate the stability and oscillatory behavior of a fundamentally unstable particle whose potential energy is harmonically modulated. The only vibrational modes, or Floquet forms, that are stable, can be described on primitive time cells by periodic eigenfunctions whose shapes and spectral energy densities are analytically predicted by the dimensionless Schrödinger equation of a quantum harmonic oscillator. We suggest this elementary mechanism is responsible for the orbital quantization of the radiating collapsing electron of the atomic ``planetary'' model and find Bohr's successful predictions of Hydrogen spectral series can be derived with simple scaling arguments.