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Indian Journal of Advanced Physics

Quantized Atomic Energies Emerge from Classical Subatomic Particle Simulations: Discovery of Quantum Effects enclosed in Classical Mechanics explaining Atomic Spectral Lines

S. Venkatesan

Published Oct 27, 2026• 0 citations
Publisher

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 atoms energy as a function of time reveals quantised, discrete energy values rather than the continuous energies expected in classical simulations. Changes in an atoms 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 atoms quantum energy shifts. Only one electrons 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.

DOI
10.54105/ijap.b1076.06021026

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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 atoms energy as a function of time reveals quantised, discrete energy values rather than the continuous energies expected in classical simulations. Changes in an atoms 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 atoms quantum energy shifts. Only one electrons 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.
Classical subatomic particles simulations were applied to protons, neutrons and electrons to simulate a complete atom using pseudo potentials to simulate nucleus and electrons distributed around nucleus. Molecular dynamics algorithms were applied to subatomic particles to simulate a complete atom for Hydrogen, Carbon and Uranium atoms that were reported in previous studies. Further analysis of energies of Carbon atom reveals that atom has quantized discrete energy values rather than continuous energies as expected in classical simulations. Changes in atom's total energy were observed to be in step changes going to higher/lower energy states and energy values are observed to be in quantized rather than continuous. Electrons energy profiles was observed during the atom's quantum energy shifts and only one electron got affected that has step change in its energies, for short duration, leaving other electrons unaffected. To observe similar phenomenon in other atoms, Fluorine, Magnesium and Chlorine atom were considered in this study and found to have similar quantized discrete energy values properties. This study implements subatomic particles simulations using classical mechanics that explains why atom's energies are quantized in nature as observed in discrete lines in atomic emission/absorption spectrum for atoms.
This paper re-examines the mechanism of electron motion inside atoms and the causes of photon radiation and photon absorption, abandoning the inherent cognition of fixed electron orbits and quantum transitions in traditional atomic physics. It clarifies that electrons have no physical fixed orbits; orbits are only imaginary concepts constructed for convenience of description, not objective physical realities. With mass, electrons possess inertia and kinetic energy. Under the three-force equilibrium of Coulomb force, electromagnetic force and inertial effect, electrons naturally move in elliptical trajectories rather than regular circles. When an electron moves along an elliptical trajectory, it naturally passes through low-energy regions near the atomic nucleus and high-energy regions far from the nucleus. This change in position arises entirely from its own inertia, involving only the conversion between kinetic energy and potential energy. The electron neither gains nor loses total energy, so it emits no photons and undergoes no energy-level change. An electron loses total energy when emitting a photon outward, and transitions smoothly and continuously to a lower overall motion range under mechanical equilibrium and inertia. Meanwhile, an electron can also absorb external photons and gain energy; its total energy increases, and it similarly expands smoothly to a higher motion range. Photon energy is indivisible and can only be emitted or absorbed as a complete unit. This is the fundamental reason why atoms show discrete emission and absorption spectra. Electron motion is entirely smooth and continuous; instantaneous quantum transitions assumed in traditional physics do not exist. Based on classical mechanics and energy conservation, this paper unifies the laws of macroscopic celestial bodies and microscopic particles, and reconstructs an atomic motion model closer to the essential nature of physics.
The mere existence of stable atoms, and their arrangement into many-atom nanoscale structures, can only be explained by the laws of quantum mechanics. Indeed, the accumulated evidence regarding the internal structure of atoms motivated the formulation of quantum mechanics at the early twentieth century. Here we focus on single-electron (hydrogen-like) atoms. The dominance of the Coulomb central potential between the electron and nucleus, translates into a simple Schrödinger equation for their relative position distribution. Solving rigorously this equation reveals quantized energy levels, which explains the emission spectra of hydrogen-like atoms (Rydberg formula). The corresponding stationary probability density distributions for the electron around the nucleus are reminiscent of the Bohr model, where classical trajectories (orbits) are replaced by single-electron wave functions (orbitals). The degeneracies of different orbitals, associated with three quantum numbers, will later turn out to be critical for understanding many-electron atoms and the periodic table of the elements.
This paper fully recognizes repeatable experimental facts related to atomic spectral observations electron shell arrangement and energy level transitions and respects all observed phenomena. It does not deny the statistical laws corresponding to energy level effects and the Pauli exclusion effect. The core purpose of this paper is to correct the long standing model inversion misunderstanding in quantum theory that is treating artificial definitions and mathematical approximation diagrams used by humans to simplify calculation and facilitate academic communication directly as physical reality in the microscopic world. This paper clearly distinguishes practical calculation rules from underlying physical mechanisms. Induced laws for human deduction and analysis cannot replace the true interaction nature of particles. This paper constructs a microscopic atomic picture based purely on mechanical balance with the core conclusions as follows. Atomic energy levels are not discrete geometric thin lines but continuous spherical potential energy intervals centered on atomic nuclei. The steady state of electron orbits arises from the combined balance of Coulomb repulsion and nuclear attraction instead of being preset in advance. The textbook diagrams showing intersecting orbits and dynamic avoidance of electrons are only effects of planar simplified drawing and do not represent the true microscopic state. Electrons in the same layer maintain stable equal spacing by Coulomb repulsion but spherical surfaces of inner and outer layers have different potential energy gradients leading to obvious differences in energy level gaps and finally differentiated transition spectra. Segmentation of visible light spectra originates from the difference in photoreception of cone cells in human eyes. Man is the measure of all things. Classification of spectra and energy levels by discrete criteria comes from human observational induction while natural ontology remains continuous. The Pauli exclusion effect is not an innate axiom of the universe but a natural mechanical result formed jointly by three dimensional space Coulomb repulsion and potential energy balance. This paper takes mechanical causality as the only main line to uniformly explain atomic energy levels spectral features and electron arrangement rules. All inferences strictly rely on experimental observations.
This chapter discusses the physical properties of atoms and molecules, which are quantized. This means that they can only take certain discrete values rather than a full range of continuously varying values. The chapter examines the quantized energy levels of a molecule. These are called stationary states, which describe an energy that is independent of time. The chapter also outlines the procedure for constructing a quantum mechanical Hamiltonian, which includes writing down the complete and classical expression for the energy of the system. The chapter reviews the general approach to the determination of energy levels of a physical system. This involves two stages: First, the appropriate Hamiltonian is defined and, in a second step, the eigenfunctions and eigenvalues of the Hamiltonian are determined. The chapter also discusses the Schrödinger equation, which can only be solved for one-body systems.