Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

The Real Nature of Atomic Energy Levels and Electron Orbits

Jiaqing Yan

Published Sep 22, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.5281/zenodo.22885606

Related papers

Study on the Physical Eigenstate of Electron Real Orbit and the Mechanism Defect of Quantum Probability Interpretation

Jiaqing Yan

The mainstream interpretation of quantum mechanics adopts the probability cloud interpretation to describe the motion of extranuclear electrons. It denies the continuous real orbit of electrons, attributes atomic magnetic moment to the intrinsic property of particles, and explains atomic spectra as traceless spontaneous energy level transitions of electrons. It presupposes that atoms can only absorb photons with energy strictly equal to the energy level difference. Based on the unified physical framework of the Light Source Theory, this paper demonstrates that extranuclear electrons have stable and continuous real orbits of revolution. The centripetal force of the electron orbit is dominated by Coulomb attraction, and gravitational force at atomic scale is negligible. The centripetal force is always perpendicular to the instantaneous motion direction of the electron and does not do work. Only mutual conversion between kinetic energy and electric potential energy inside the system occurs on the elliptical orbit, and there is no spontaneous radiation loss in steady revolution. The constraint for an atom to absorb a photon is that the polarization angle of the photon matches the polarization orientation of the electron orbit, and there is no requirement for the photon energy to correspond to the energy level difference. As long as the polarization matches, photons of any energy can be absorbed. Low energy photons can be absorbed multiple times to accumulate energy gradually, and high energy photons can also be absorbed once to raise the stored energy directly. The orbit adjusts continuously with the change of energy. When the accumulated energy reaches the inherent energy level limit of the atomic system, the original orbit configuration can no longer bear higher stored energy, and the atom releases characteristic photons with fixed energy to form discrete spectra. There is no one to one energy equivalence relationship between absorbed photons and emitted photons, which is the core reason why atomic spectra can be observed and distinguished from background light in the environment. The magnetic field of permanent magnets and the magnetization of materials originate from the directional orbital revolution of electrons. The probability cloud and traceless transition are only mathematical fitting schemes adapted to spectral data rather than physical reality. This interpretation has inherent contradictions such as unexplainable origin of magnetic field, equivalent superluminal transition and Coulomb gravitational collapse. Macroscopic and microscopic phenomena follow unified causal laws, and there are no special motion rules exclusive to quantum systems. Atoms present a spherical three dimensional structure. Extranuclear electrons revolve three dimensionally in spherical space under the three force balance of Coulomb force inertia effect and magnetic force which are perpendicular to each other in pairs. If there is no real orbit, magnetic force has no source of generation, and electrons can only move in a single plane, which cannot explain the spherical shape of atoms. This constitutes an important question to the probability cloud interpretation.

•Oct 26, 2026•0 citations

On the Essence of Electron Motion Without Fixed Orbits and Energy Quantization of Photon Radiation

Jiaqing Yan

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.

•May 14, 2026•0 citations

Unified Principle of Macro and Micro Motion: Steady-State Elliptical Orbits and Corrections to Paradoxes in Quantum Theory

Jiaqing Yan

Existing physics artificially separates the fundamental laws governing the motion of macroscopic celestial bodies and microscopic particles. To resolve the orbit collapse dilemma of classical atomic models, it introduces assumptions such as superposition states and instantaneous quantum transitions, which generate multiple logical contradictions that violate the law of conservation of energy and the ultimate speed limit of light. Based on the Light Primitive Theory, this paper establishes a unified orbital motion system for macro and micro objects. It demonstrates that perfect geometric circles are merely mathematical idealizations, while three-dimensional closed spatial curves represent the long-term stable motion form of electrons at the microscale; two-dimensional planar ellipses are only simplified motion states of macroscopic celestial bodies. This paper points out that closed curves rely on the bidirectional conversion of kinetic energy and potential energy to achieve near-lossless motion with built-in energy storage and anti-interference capabilities. Electrons are constrained by three mutually orthogonal forces, resulting in motion trajectories that cannot be confined to a single plane. All massive physical entities (including electrons) follow unified laws of orbital energy conversion. Meanwhile, this paper systematically exposes the fatal flaws of existing quantum transition theories: instantaneous transitions inevitably involve superluminal motion, displacement without energy exchange contradicts mechanical logic, and superposition states fail to explain the motion mechanisms of physical particles. This research indicates that long-term stable motion in the universe follows closed curved paths, while linear motion is only a transient transitional state. Certain foundational quantum hypotheses are makeshift, erroneous theories created to patch gaps in older physical frameworks.

•Jul 17, 2026•0 citations

Quantum Measurement: A New View

H. J. Spencer

This report investigates the flawed foundations of standard quantum theory based on a misunderstanding of the role of measurement. The report is major part of a research programme (UET) based on a new theory of the electromagnetism (EM), centered exclusively on the interaction between electrons. All the previous papers to date in this series have presented a realistic view of the dynamics of two or more electrons as they interact only between themselves. This paper now posits a theory of how this microscopic activity is perceived by human beings in attempting to extract information about atomic systems. The standard theory of quantum mechanics (QM) is constructed on only how the micro-world appears to macro measurements - as such, it cannot offer any view of how the foundations of the world are acting when humans are not observing it (the vast majority of the time) - this has generated almost 100 years of confusion and contradiction at the very heart of physics. All human beings (and all our instruments) are vast collections of electrons, our information about atomic-scale can only be obtained destructively and statistically. This theory now extends the realistic model of digital electrons by adding an explicit measurement model of how our macro instruments interfere with nature's micro-systems when such attempts result in human-scale information. The focus here is on the connection between the micro-world (when left to itself) and our mental models of this sphere of material reality, via the mechanism of atomic measurements. The mathematics of quantum mechanics reflects the eigenvalues of the combined target system plus equipment used for measurement together. Therefore, QM has constructed a theory that inseparably conflates the ontological and epistemological views of nature. This standard approach fails to examine isolated target systems alone. It is metaphysically deficient. This investigation concludes that the Quantum State function (Ψ) is not a representation of physical reality, within a single atom, but a generator function for producing the average statistical results on many atoms of this type. In contrast, the present theory builds on the physical reality of micro-states of single atoms, where (in the case of hydrogen), a single electron executes a series of fixed segments (corresponding to the micro-states) across the atom between a finite number of discrete interactions between the electron and one of the positrons in the nucleus. The set of serial segments form closed trajectories with real temporal periods, contra to Heisenberg’s ‘papal’ decree banning such reality because of his need to measure position and momentum at all times. This is the first paper in the multi-paper series (UET7n), which is dedicated to analyzing, criticizing and replacing existing theories of quantum mechanics.

•Apr 1, 2017•0 citations

Quantum Mechanics

David Bensimon

Chapter 4 deals with Quantum Mechanical (QM) phenomena. The first section describes the first attempts at quantization of energy, momentum, angular momentum, etc. We start with Plank's solution to the black-body problem, introducing the concept of photons: discrete packets of electromagnetic energy. We show how Plank's description of black-body radiation is perfectly fit by the cosmic microwave radiation, providing the strongest evidence for the Big-Bang at the origin of the Universe. We then describe Bohr's solution to the paradoxical stability of atoms, introducing quantization of angular momentum (or action) and correctly predicting the energy levels of the hydrogen atom. We show how Einstein used Plank's idea to explain the photo-electric effect (an effect exploited in CCD cameras and solar cells) and how he used Bohr's understanding of energy levels in atoms to provide an intuitive explanation of Plank's law. Einstein insight opened the way to the field of spectroscopy and the development of the laser. In the second section, following the lead of Dirac, we show that QM is equivalent to Linear Algebra in the space of complex functions (which describe the state of the system). We show that Schrödinger's equation is a natural consequence of that description, once the relation between energy and frequency established by Plank (for photons) and de Broglie (for particles) is taken into account. In the context of the chiral ammonia molecule we discuss the queerness of QM which describes physical systems as superposition of states (such as left and right chirality state of a molecule, dead and alive cat). We show that this queerness is nonetheless supported by experiments and is behind much of our technology: masers and lasers, atomic clocks, semiconductors (diodes, transistors, etc.). In the following section we introduce the representation of operators in QM (the equivalent of matrices in linear algebra): momentum, position, energy, etc. which correspond to measurements on the system. We show that the non-commutability of some operators (common with matrix operations) leads to Heisenberg uncertainty principle: the position and momentum of a particle cannot be determined with absolute precision. We discuss the solution of Schrödinger's equation for free particles demonstrating their equivalence with EM phenomena: particles undergo refraction and diffraction, exemplifying the particle/wave duality inherent to QM systems. We discuss QM tunneling and its use in the Scanning Tunneling Microscope. In the following section we study Dirac's equation: the successful attempt by Dirac to unify QM with Einstein's relativity, with the resulting prediction of anti-particles and spin. We then solve for the energy levels of electrons in the hydrogen atom (from Schrödinger's equation) and show that the existence of spin profoundly affects the behavior of electrons in an atom: they cannot share the same energy level, a rule known as Pauli's exclusion principle. Pauli's principle is central to the understanding of the chemical properties of atoms and fully explains Mendeleev's periodic table of the elements. In the next section we discuss along with two exactly soluble systems (diatomic rotational and vibrational levels), various approximations used to study systems (e.g. molecules) for which there are no analytical solutions. In particular, we introduce Pauling's variational approach, Hückel molecular orbital theory and time independent perturbation theory. We apply those approaches to determine the energy levels in alkenes, in multi-electron atoms and in systems under constant electric or magnetic field (such as in Magnetic Resonance Imaging). In the last section we discuss time dependent perturbation theory. We use it to establish the rules allowing for transitions between energy levels and revisit Einstein description of absorption/emission phenomena.

CRC Press eBooks•Nov 17, 2021•0 citations

A New Interpretation of Electron Motion in Hydrogen Atoms via Attosecond Detection

Jiaqing Yan

The Copenhagen interpretation of traditional quantum mechanics describes the behaviour of electrons within atoms using probability clouds, superposition states and instantaneous transitions, denying that electrons have definite motion orbits and continuous evolutionary processes. Based on the author’s two previous core research findings on the continuous motion of extranuclear electrons, this paper cites experimental data from state of the art attosecond ultrashort laser pulses. Through time scale matching, reconstruction of motion sequences and logical deduction constrained by experimental results, it demonstrates that electrons inside atoms possess stable, continuous and periodic orbital motion characteristics. This paper puts forward mechanical challenges to the probability cloud picture and the hypothesis of instantaneous transitions: since electrons have rest mass, any abrupt change in position must be accompanied by corresponding instantaneous external forces as well as energy input or output. An instantaneous transition implies that position change occurs without consuming finite time, which is equivalent to superluminal displacement. This hypothesis lacks a corresponding dynamical mechanism and thus involves profound physical contradictions. In contrast, the continuous motion model yields a complete and self consistent physical explanation solely based on the known Coulomb electrostatic attraction, Lorentz magnetic force and electron inertia. Current attosecond detection results are fully adequate to validate the reasonableness of prior calculations of hydrogen atom orbits and confirm the physical reality of the continuous orbital motion of electrons. This poses a fundamental challenge to the traditional interpretation featuring probability clouds and instantaneous transitions with no intermediate processes.

•Sep 10, 2026•0 citations
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.
The mainstream interpretation of quantum mechanics adopts the probability cloud interpretation to describe the motion of extranuclear electrons. It denies the continuous real orbit of electrons, attributes atomic magnetic moment to the intrinsic property of particles, and explains atomic spectra as traceless spontaneous energy level transitions of electrons. It presupposes that atoms can only absorb photons with energy strictly equal to the energy level difference. Based on the unified physical framework of the Light Source Theory, this paper demonstrates that extranuclear electrons have stable and continuous real orbits of revolution. The centripetal force of the electron orbit is dominated by Coulomb attraction, and gravitational force at atomic scale is negligible. The centripetal force is always perpendicular to the instantaneous motion direction of the electron and does not do work. Only mutual conversion between kinetic energy and electric potential energy inside the system occurs on the elliptical orbit, and there is no spontaneous radiation loss in steady revolution. The constraint for an atom to absorb a photon is that the polarization angle of the photon matches the polarization orientation of the electron orbit, and there is no requirement for the photon energy to correspond to the energy level difference. As long as the polarization matches, photons of any energy can be absorbed. Low energy photons can be absorbed multiple times to accumulate energy gradually, and high energy photons can also be absorbed once to raise the stored energy directly. The orbit adjusts continuously with the change of energy. When the accumulated energy reaches the inherent energy level limit of the atomic system, the original orbit configuration can no longer bear higher stored energy, and the atom releases characteristic photons with fixed energy to form discrete spectra. There is no one to one energy equivalence relationship between absorbed photons and emitted photons, which is the core reason why atomic spectra can be observed and distinguished from background light in the environment. The magnetic field of permanent magnets and the magnetization of materials originate from the directional orbital revolution of electrons. The probability cloud and traceless transition are only mathematical fitting schemes adapted to spectral data rather than physical reality. This interpretation has inherent contradictions such as unexplainable origin of magnetic field, equivalent superluminal transition and Coulomb gravitational collapse. Macroscopic and microscopic phenomena follow unified causal laws, and there are no special motion rules exclusive to quantum systems. Atoms present a spherical three dimensional structure. Extranuclear electrons revolve three dimensionally in spherical space under the three force balance of Coulomb force inertia effect and magnetic force which are perpendicular to each other in pairs. If there is no real orbit, magnetic force has no source of generation, and electrons can only move in a single plane, which cannot explain the spherical shape of atoms. This constitutes an important question to the probability cloud interpretation.
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.
Existing physics artificially separates the fundamental laws governing the motion of macroscopic celestial bodies and microscopic particles. To resolve the orbit collapse dilemma of classical atomic models, it introduces assumptions such as superposition states and instantaneous quantum transitions, which generate multiple logical contradictions that violate the law of conservation of energy and the ultimate speed limit of light. Based on the Light Primitive Theory, this paper establishes a unified orbital motion system for macro and micro objects. It demonstrates that perfect geometric circles are merely mathematical idealizations, while three-dimensional closed spatial curves represent the long-term stable motion form of electrons at the microscale; two-dimensional planar ellipses are only simplified motion states of macroscopic celestial bodies. This paper points out that closed curves rely on the bidirectional conversion of kinetic energy and potential energy to achieve near-lossless motion with built-in energy storage and anti-interference capabilities. Electrons are constrained by three mutually orthogonal forces, resulting in motion trajectories that cannot be confined to a single plane. All massive physical entities (including electrons) follow unified laws of orbital energy conversion. Meanwhile, this paper systematically exposes the fatal flaws of existing quantum transition theories: instantaneous transitions inevitably involve superluminal motion, displacement without energy exchange contradicts mechanical logic, and superposition states fail to explain the motion mechanisms of physical particles. This research indicates that long-term stable motion in the universe follows closed curved paths, while linear motion is only a transient transitional state. Certain foundational quantum hypotheses are makeshift, erroneous theories created to patch gaps in older physical frameworks.
This report investigates the flawed foundations of standard quantum theory based on a misunderstanding of the role of measurement. The report is major part of a research programme (UET) based on a new theory of the electromagnetism (EM), centered exclusively on the interaction between electrons. All the previous papers to date in this series have presented a realistic view of the dynamics of two or more electrons as they interact only between themselves. This paper now posits a theory of how this microscopic activity is perceived by human beings in attempting to extract information about atomic systems. The standard theory of quantum mechanics (QM) is constructed on only how the micro-world appears to macro measurements - as such, it cannot offer any view of how the foundations of the world are acting when humans are not observing it (the vast majority of the time) - this has generated almost 100 years of confusion and contradiction at the very heart of physics. All human beings (and all our instruments) are vast collections of electrons, our information about atomic-scale can only be obtained destructively and statistically. This theory now extends the realistic model of digital electrons by adding an explicit measurement model of how our macro instruments interfere with nature's micro-systems when such attempts result in human-scale information. The focus here is on the connection between the micro-world (when left to itself) and our mental models of this sphere of material reality, via the mechanism of atomic measurements. The mathematics of quantum mechanics reflects the eigenvalues of the combined target system plus equipment used for measurement together. Therefore, QM has constructed a theory that inseparably conflates the ontological and epistemological views of nature. This standard approach fails to examine isolated target systems alone. It is metaphysically deficient. This investigation concludes that the Quantum State function (Ψ) is not a representation of physical reality, within a single atom, but a generator function for producing the average statistical results on many atoms of this type. In contrast, the present theory builds on the physical reality of micro-states of single atoms, where (in the case of hydrogen), a single electron executes a series of fixed segments (corresponding to the micro-states) across the atom between a finite number of discrete interactions between the electron and one of the positrons in the nucleus. The set of serial segments form closed trajectories with real temporal periods, contra to Heisenberg’s ‘papal’ decree banning such reality because of his need to measure position and momentum at all times. This is the first paper in the multi-paper series (UET7n), which is dedicated to analyzing, criticizing and replacing existing theories of quantum mechanics.
Chapter 4 deals with Quantum Mechanical (QM) phenomena. The first section describes the first attempts at quantization of energy, momentum, angular momentum, etc. We start with Plank's solution to the black-body problem, introducing the concept of photons: discrete packets of electromagnetic energy. We show how Plank's description of black-body radiation is perfectly fit by the cosmic microwave radiation, providing the strongest evidence for the Big-Bang at the origin of the Universe. We then describe Bohr's solution to the paradoxical stability of atoms, introducing quantization of angular momentum (or action) and correctly predicting the energy levels of the hydrogen atom. We show how Einstein used Plank's idea to explain the photo-electric effect (an effect exploited in CCD cameras and solar cells) and how he used Bohr's understanding of energy levels in atoms to provide an intuitive explanation of Plank's law. Einstein insight opened the way to the field of spectroscopy and the development of the laser. In the second section, following the lead of Dirac, we show that QM is equivalent to Linear Algebra in the space of complex functions (which describe the state of the system). We show that Schrödinger's equation is a natural consequence of that description, once the relation between energy and frequency established by Plank (for photons) and de Broglie (for particles) is taken into account. In the context of the chiral ammonia molecule we discuss the queerness of QM which describes physical systems as superposition of states (such as left and right chirality state of a molecule, dead and alive cat). We show that this queerness is nonetheless supported by experiments and is behind much of our technology: masers and lasers, atomic clocks, semiconductors (diodes, transistors, etc.). In the following section we introduce the representation of operators in QM (the equivalent of matrices in linear algebra): momentum, position, energy, etc. which correspond to measurements on the system. We show that the non-commutability of some operators (common with matrix operations) leads to Heisenberg uncertainty principle: the position and momentum of a particle cannot be determined with absolute precision. We discuss the solution of Schrödinger's equation for free particles demonstrating their equivalence with EM phenomena: particles undergo refraction and diffraction, exemplifying the particle/wave duality inherent to QM systems. We discuss QM tunneling and its use in the Scanning Tunneling Microscope. In the following section we study Dirac's equation: the successful attempt by Dirac to unify QM with Einstein's relativity, with the resulting prediction of anti-particles and spin. We then solve for the energy levels of electrons in the hydrogen atom (from Schrödinger's equation) and show that the existence of spin profoundly affects the behavior of electrons in an atom: they cannot share the same energy level, a rule known as Pauli's exclusion principle. Pauli's principle is central to the understanding of the chemical properties of atoms and fully explains Mendeleev's periodic table of the elements. In the next section we discuss along with two exactly soluble systems (diatomic rotational and vibrational levels), various approximations used to study systems (e.g. molecules) for which there are no analytical solutions. In particular, we introduce Pauling's variational approach, Hückel molecular orbital theory and time independent perturbation theory. We apply those approaches to determine the energy levels in alkenes, in multi-electron atoms and in systems under constant electric or magnetic field (such as in Magnetic Resonance Imaging). In the last section we discuss time dependent perturbation theory. We use it to establish the rules allowing for transitions between energy levels and revisit Einstein description of absorption/emission phenomena.
The Copenhagen interpretation of traditional quantum mechanics describes the behaviour of electrons within atoms using probability clouds, superposition states and instantaneous transitions, denying that electrons have definite motion orbits and continuous evolutionary processes. Based on the author’s two previous core research findings on the continuous motion of extranuclear electrons, this paper cites experimental data from state of the art attosecond ultrashort laser pulses. Through time scale matching, reconstruction of motion sequences and logical deduction constrained by experimental results, it demonstrates that electrons inside atoms possess stable, continuous and periodic orbital motion characteristics. This paper puts forward mechanical challenges to the probability cloud picture and the hypothesis of instantaneous transitions: since electrons have rest mass, any abrupt change in position must be accompanied by corresponding instantaneous external forces as well as energy input or output. An instantaneous transition implies that position change occurs without consuming finite time, which is equivalent to superluminal displacement. This hypothesis lacks a corresponding dynamical mechanism and thus involves profound physical contradictions. In contrast, the continuous motion model yields a complete and self consistent physical explanation solely based on the known Coulomb electrostatic attraction, Lorentz magnetic force and electron inertia. Current attosecond detection results are fully adequate to validate the reasonableness of prior calculations of hydrogen atom orbits and confirm the physical reality of the continuous orbital motion of electrons. This poses a fundamental challenge to the traditional interpretation featuring probability clouds and instantaneous transitions with no intermediate processes.