Revisiting the Bohr Model of the Atom through Brownian Motion of the Electron

• URL: http://arxiv.org/abs/2412.19918v4
• Date: Sat, 22 Feb 2025 17:58:31 GMT
• Title: Revisiting the Bohr Model of the Atom through Brownian Motion of the Electron
• Authors: Vasil Yordanov,
• Abstract summary: We refine the Bohr model of the hydrogen atom by describing the motion of the electron through a single real-valued process.<n>Our approach derives the electron's equation of motion from the Fokker-Planck equation while ensuring the particle always maintains a definite - albeit random - position.<n>We show that these equations reproduce the correct average radial and angular quantum kinetic, matching operator-based predictions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this work, we refine the Bohr model of the hydrogen atom by describing the motion of the electron through a single real-valued stochastic process, effectively realizing Brownian motion under the Born rule. Our approach derives the electron's stochastic equation of motion from the Fokker-Planck equation while ensuring the particle always maintains a definite - albeit random - position. This feature obviates the need for wave function collapse as invoked in the Copenhagen interpretation. Instead, the wave function serves as a tool to compute the electron's drift velocity. Building on this, we develop modified stochastic equations in spherical coordinates, tailored to the spherical symmetry of the hydrogen atom. We show that these equations reproduce the correct average radial and angular kinetic energies, matching operator-based quantum mechanical predictions. Numerical simulations confirm the stability of electron trajectories and, as expected, recover the probability distribution prescribed by the Born rule. At very short timescales, however, single-electron probability distributions may deviate from wave function-based predictions due to insufficient ensemble averaging. Taken together, these findings offer an alternative perspective on atomic structure and highlight the potential of using wave function-derived drift velocities within a single stochastic process to capture quantum dynamics in the hydrogen atom.

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