Quantized Atomic Energies Emerge from Classical Subatomic Particle Simulations: Discovery of Quantum Effects enclosed in Classical Mechanics explaining Atomic Spectral Lines
Shanmuga Sundaram Venkatesan
Dr. Shanmuga Sundaram Venkatesan, Independent Researcher, Sahasrara Research, Tirupati, India.
Manuscript received on 07 May 2026 | First Revised Manuscript received on 14 May 2026 | Second Revised Manuscript received on 16 September 2026 | Manuscript Accepted on 15 October 2026 | Manuscript published on 30 October 2026 | PP: 1-6 | Volume-6 Issue-2, October 2026 | Retrieval Number: 100.1/ijap.B107606021026 | DOI: 10.54105/ijap.B1076.06021026
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© The Authors. Published by Lattice Science Publication (LSP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: Classical subatomic particle simulations were applied to protons, neutrons, and electrons to simulate an individual atom using pseudo-potentials to simulate the nucleus and electrons distributed around the nucleus. We applied molecular dynamics algorithms to subatomic particles to simulate complete atoms of Hydrogen, Carbon, and Uranium, as reported in our previous studies. Investigation of the Carbon atom’s energy as a function of time reveals quantised, discrete energy values rather than the continuous energies expected in classical simulations. Changes in an atom’s total energy were found to occur in discrete steps as it transitionsto higher/lower energy states, and the energy values are observed to be quantised rather than continuous. Further analysis examined individual electron energies to determine how electrons behave during an atom’s quantum energy shifts. Only one electron’s energy profile had undergone a step change, leaving the other five electrons unaffected in a Carbon atom. To study the energy quantisation property in other atoms, the Fluorine, Magnesium, and Chlorine atoms were considered and found to exhibit similar quantised, discrete energy properties. The energy quantisation property of an individual atom was already accounted for in classical mechanics/models. This study uses classicalmechanics simulations of subatomic particles to investigate why atomic energies are quantised in nature, as observed in discrete lines in atomic emission/absorption spectra.
Keywords: Subatomic Particle Simulations, Classical Mechanics Energy Quantized, Atomic Emission Spectra, Atom’s Energies Quantized, Energy Quantization.
Scope of the Article: Atomic, Molecular, and Optical Physics