Advanced computational methods for simulating the classical hydrogen atom in stochastic electrodynamics
Stochastic electrodynamics (SED) is a theory of nature seeking to derive key aspects of quantum mechanics and quantum electrodynamics from a purely classical physics perspective. While SED has been successful in many areas, it has had mixed success when addressing the classical hydrogen atom bathed in classical electromagnetic zero-point radiation. Because analytical approaches are largely intractable, advanced numerical simulation methods are required. To address this, we develop a pseudo-wave formulation that integrates the solid angle in k-space utilizing symmetry, resulting in a significantly reduced memory footprint and lower computational overhead for generating the zero-point radiation spectrum. This optimization is paired with a logarithmic frequency grid, a sliding window tracking the instantaneous Keplerian frequency, and a Tukey smoothing function to eliminate discrete force discontinuities. Integrated via an adaptive RK4 algorithm with step-doubling across highly dense grids of up to 100-million bins, these techniques demonstrate the asymptotic convergence of ensemble stability. We show that increasing grid resolution in the high-frequency domain systematically mitigates artificial electron decay, yielding a simulated probability density function that closely aligns with the quantum mechanical ground state P(r). Crucially, the simulations exhibit stable, low-eccentricity orbits without any observed atomic ionization events.