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

Wave Function Behind Hydrogen Atom Gate

Dragan Popovic

Published May 7, 2026• 0 citations
Publisher

Abstract

Working hypothesis: This paper proposes an interpretive physical model in which a single hydrogen atom acts as an oscillating gate for electron tunneling. The probability peak behind the gate is shifted away from the gate face — a result consistent with standard quantum mechanics but here given a physical mechanism. The wave function is treated as a mathematical tool tracking physical reality, not as the reality itself. These proposals are offered as a working hypothesis for discussion, not as established physics.

DOI
10.5281/zenodo.20074340

Related papers

A New Physical Interpretation of the de Broglie Wave

Dragan Popovic

This paper proposes a dynamical interpretation of the de Broglie wave in which the electron alternates between relatively localized and relatively delocalized propagation phases. The electron's rest mass is treated throughout as a conserved invariant. The proposal does not involve rest mass conversion. What may oscillate is the spatial configuration of the electron's quantized energy states — the way energy organizes itself around the fixed core — not the core itself. The proposal is motivated by a numerical observation: the orbital frequency and the de Broglie frequency of the electron in the hydrogen ground state are exactly equal, computed independently from classical mechanics and quantum wave theory. The equality itself is not new. What is proposed is its physical meaning: one complete localization–delocalization cycle occurs per orbital period. The interpretation is consistent with the Heisenberg uncertainty principle and the Schrödinger equation. Several observations from established physics are discussed as consistent with the proposed framework. The proposal is presented as an interpretive extension of standard quantum mechanics, not a replacement.

•May 17, 2026•0 citations

What Is a Wave Function?

William J. Mullin

The wave function gives probabilities, but is it a real physical quantity, as in the ontic interpretation of quantum mechanics, or just a measure of human belief about a physical system, as in an epistemic interpretation? These questions are introduced by treating Schrödinger’s cat and Wigner’s friend. An important question is whether quantum mechanics applies to macroscopic objects, for example, cats. SQUID experiments have been performed that see quantum interference in very large objects, whereas with most macroscopic objects quantum interference disappears because of decoherence. Various views of the meaning of quantum mechanics are discussed: the Copenhagen interpretation, continuous spontaneous localization, Everett’s many-worlds interpretation, Bohm’s hidden-variable model, and quantum Bayesianism. The latter holds that the wave function represents one’s best belief about the state of a quantum system, rather than an actual physical property. This leads to discussions of recent theories and experiments explicitly designed to test wave function reality.

Oxford University Press eBooks•Mar 16, 2017•0 citations

Methodological Aspects of Teaching Quantum Mechanics Using the Example of The Hydrogen Atom

M. K.

This article explores methodological aspects of teaching quantum mechanics in higher education within the framework of physics and mathematics programs. Particular attention is given to the challenge’s students face in mastering fundamental concepts due to the high level of abstraction inherent in the subject. The hydrogen atom model is considered as a focal example – being both conceptually significant and visually illustrative in demonstrating the principles of quantum theory. The core emphasis is placed on the interpretation of the wave function and its physical meaning through the concept of probability density. Methods for visualizing electron wave states are discussed, alongside graphical representations of probability densities corresponding to various quantum numbers. The relationship between the analytical solutions of the Schrodinger equation and the physical interpretation of these results is substantiated. Special attention is also devoted to developing students’ understanding of the probabilistic nature of quantum systems, as well as their ability to apply mathematical tools for modeling and interpreting quantum states. Didactic approaches are proposed to enhance students’ abstract thinking and intuitive grasp of quantum principles.

International Journal of Pedagogics•Jul 1, 2025•0 citations

An Equation Similar to the Schroedinger Equation for the Atom with an Electron, Which Moves, from the Point of View of an Observer

Edigles Guedes

When we conduct a thought experiment, in which the observer moves and can see the model for Schroedinger wave equation of atom with one electron, we create a wave function and calculate its wave eigenfunction acceptable, in spherical coordinates.

•Mar 1, 2013•0 citations

In Search of Schroedinger's Electron and Einstein's Atom Too !

Jean Louis Van Belle

This article explores a possible physical interpretation of the wavefunction. It zooms in on the physical model it implies for an electron in free space (further building on Schroedinger's ideas in regard to the apparent Zitterbewegung of an electron), but then also discusses the wavefunction for particles (including non-charged particles) in general. While it basically concludes that the mainstream interpretation of quantum physics (the Copenhagen interpretation) is and remains the most parsimonious explanation, it also argues that one or two extra assumptions – the wavefunction as a two-dimensional self-sustaining electromagnetic or gravitational oscillation in space – would make more frivolous explanations (many worlds, pilot wave, etcetera) redundant.

•Sep 1, 2018•0 citations

Problems of Quantum Mechanics (UET7B)

H. J. Spencer

This paper re-opens the debate on the failure of quantum mechanics to provide an understandable view of micro-reality. A critique is offered of the commonly accepted ‘Copenhagen Interpretation’ of a theory that is only a mathematical approach to the level of reality characterized by atoms and electrons. This critique is based on the oldest approach to thinking about nature for over 2500 years, known as Natural Philosophy. Quantum mechanics (QM) was developed over the first quarter of the 20th Century, when scientists were enthralled by a new philosophy known as Positivism, whose foundations were based on the assumption that material objects exist only when measured by humans – this central assumption conflates epistemology (knowledge) with ontology (existence). The present critique rejects this human-centered view of reality by assuming material reality has existed long before (and will persist long after) human beings (“Realism”). The defensive view that the micro-world is too different to understand using regular thinking (and only a mathematical approach is possible) is rejected totally. At least 12 earlier QM interpretations are critically analyzed, indicating the broad interest in “what does QM mean?” The standard theory of quantum mechanics is thus 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 - this has generated almost 100 years of confusion and contradiction at the very heart of physics. Significantly, we live in a world that is not being measured by scientists but is interacting with itself and with us. QM has failed to provide explanations: only recipes (meaningless equations), not insights. Physics has returned to the pre-Newtonian world of Ptolemaic phenomenology: only verifiable numbers without real understanding. The focus needs to be on an explicit linkage between the micro-world, when left to itself, and our mental models of this sphere of material reality, via the mechanism of measurement. This limits the role of measurement to confirming our mental models of reality but never confusing these with a direct image of ‘the thing in itself’. This implies a deep divide between reality and appearances, as Kant suggested. This paper includes an original analysis of several major assumptions that have been implicit in Classical Mechanics (CM) that were acceptable in the macroscopic domain of reality, demonstrated by its proven successes. Unfortunately, only a few of these assumptions were challenged by the developers of QM. We now show that these other assumptions are still generating confusions in the interpretation of QM and blocking further progress in the understanding of the microscopic domain. Several of these flawed assumptions were introduced by Newton to support the use of continuum mathematics as a model of nature. This paper proposes that it is the attempt to preserve continuum mathematics (especially calculus), which drives much of the mystery and confusion behind all attempts at understanding quantum mechanics. The introduction of discrete mathematics is proposed to help analyze the discrete interactions between the quintessential quantum objects: the electrons and their novel properties. A related paper demonstrates that it is possible to create a point-particle theory of electrons that explains all their peculiar (and ‘paradoxical’) behavior using only physical hypotheses and discrete mathematics without introducing the continuum mathematical ideas of fields or waves. Another (related) paper proves that all the known results for the hydrogen atom can also be exactly calculated from this new perspective with the discrete mathematics. * Surrey, B.C. Canada (604) 542-2299 spsi99@telus.net Version 2.015 08-05-2017 Begun 23-06-2008 {pp. 82, 70.2 Kw; 800 KB}

•May 1, 2017•0 citations
Working hypothesis: This paper proposes an interpretive physical model in which a single hydrogen atom acts as an oscillating gate for electron tunneling. The probability peak behind the gate is shifted away from the gate face — a result consistent with standard quantum mechanics but here given a physical mechanism. The wave function is treated as a mathematical tool tracking physical reality, not as the reality itself. These proposals are offered as a working hypothesis for discussion, not as established physics.
This paper proposes a dynamical interpretation of the de Broglie wave in which the electron alternates between relatively localized and relatively delocalized propagation phases. The electron's rest mass is treated throughout as a conserved invariant. The proposal does not involve rest mass conversion. What may oscillate is the spatial configuration of the electron's quantized energy states — the way energy organizes itself around the fixed core — not the core itself. The proposal is motivated by a numerical observation: the orbital frequency and the de Broglie frequency of the electron in the hydrogen ground state are exactly equal, computed independently from classical mechanics and quantum wave theory. The equality itself is not new. What is proposed is its physical meaning: one complete localization–delocalization cycle occurs per orbital period. The interpretation is consistent with the Heisenberg uncertainty principle and the Schrödinger equation. Several observations from established physics are discussed as consistent with the proposed framework. The proposal is presented as an interpretive extension of standard quantum mechanics, not a replacement.
The wave function gives probabilities, but is it a real physical quantity, as in the ontic interpretation of quantum mechanics, or just a measure of human belief about a physical system, as in an epistemic interpretation? These questions are introduced by treating Schrödinger’s cat and Wigner’s friend. An important question is whether quantum mechanics applies to macroscopic objects, for example, cats. SQUID experiments have been performed that see quantum interference in very large objects, whereas with most macroscopic objects quantum interference disappears because of decoherence. Various views of the meaning of quantum mechanics are discussed: the Copenhagen interpretation, continuous spontaneous localization, Everett’s many-worlds interpretation, Bohm’s hidden-variable model, and quantum Bayesianism. The latter holds that the wave function represents one’s best belief about the state of a quantum system, rather than an actual physical property. This leads to discussions of recent theories and experiments explicitly designed to test wave function reality.
This article explores methodological aspects of teaching quantum mechanics in higher education within the framework of physics and mathematics programs. Particular attention is given to the challenge’s students face in mastering fundamental concepts due to the high level of abstraction inherent in the subject. The hydrogen atom model is considered as a focal example – being both conceptually significant and visually illustrative in demonstrating the principles of quantum theory. The core emphasis is placed on the interpretation of the wave function and its physical meaning through the concept of probability density. Methods for visualizing electron wave states are discussed, alongside graphical representations of probability densities corresponding to various quantum numbers. The relationship between the analytical solutions of the Schrodinger equation and the physical interpretation of these results is substantiated. Special attention is also devoted to developing students’ understanding of the probabilistic nature of quantum systems, as well as their ability to apply mathematical tools for modeling and interpreting quantum states. Didactic approaches are proposed to enhance students’ abstract thinking and intuitive grasp of quantum principles.
This article explores a possible physical interpretation of the wavefunction. It zooms in on the physical model it implies for an electron in free space (further building on Schroedinger's ideas in regard to the apparent Zitterbewegung of an electron), but then also discusses the wavefunction for particles (including non-charged particles) in general. While it basically concludes that the mainstream interpretation of quantum physics (the Copenhagen interpretation) is and remains the most parsimonious explanation, it also argues that one or two extra assumptions – the wavefunction as a two-dimensional self-sustaining electromagnetic or gravitational oscillation in space – would make more frivolous explanations (many worlds, pilot wave, etcetera) redundant.
This paper re-opens the debate on the failure of quantum mechanics to provide an understandable view of micro-reality. A critique is offered of the commonly accepted ‘Copenhagen Interpretation’ of a theory that is only a mathematical approach to the level of reality characterized by atoms and electrons. This critique is based on the oldest approach to thinking about nature for over 2500 years, known as Natural Philosophy. Quantum mechanics (QM) was developed over the first quarter of the 20th Century, when scientists were enthralled by a new philosophy known as Positivism, whose foundations were based on the assumption that material objects exist only when measured by humans – this central assumption conflates epistemology (knowledge) with ontology (existence). The present critique rejects this human-centered view of reality by assuming material reality has existed long before (and will persist long after) human beings (“Realism”). The defensive view that the micro-world is too different to understand using regular thinking (and only a mathematical approach is possible) is rejected totally. At least 12 earlier QM interpretations are critically analyzed, indicating the broad interest in “what does QM mean?” The standard theory of quantum mechanics is thus 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 - this has generated almost 100 years of confusion and contradiction at the very heart of physics. Significantly, we live in a world that is not being measured by scientists but is interacting with itself and with us. QM has failed to provide explanations: only recipes (meaningless equations), not insights. Physics has returned to the pre-Newtonian world of Ptolemaic phenomenology: only verifiable numbers without real understanding. The focus needs to be on an explicit linkage between the micro-world, when left to itself, and our mental models of this sphere of material reality, via the mechanism of measurement. This limits the role of measurement to confirming our mental models of reality but never confusing these with a direct image of ‘the thing in itself’. This implies a deep divide between reality and appearances, as Kant suggested. This paper includes an original analysis of several major assumptions that have been implicit in Classical Mechanics (CM) that were acceptable in the macroscopic domain of reality, demonstrated by its proven successes. Unfortunately, only a few of these assumptions were challenged by the developers of QM. We now show that these other assumptions are still generating confusions in the interpretation of QM and blocking further progress in the understanding of the microscopic domain. Several of these flawed assumptions were introduced by Newton to support the use of continuum mathematics as a model of nature. This paper proposes that it is the attempt to preserve continuum mathematics (especially calculus), which drives much of the mystery and confusion behind all attempts at understanding quantum mechanics. The introduction of discrete mathematics is proposed to help analyze the discrete interactions between the quintessential quantum objects: the electrons and their novel properties. A related paper demonstrates that it is possible to create a point-particle theory of electrons that explains all their peculiar (and ‘paradoxical’) behavior using only physical hypotheses and discrete mathematics without introducing the continuum mathematical ideas of fields or waves. Another (related) paper proves that all the known results for the hydrogen atom can also be exactly calculated from this new perspective with the discrete mathematics. * Surrey, B.C. Canada (604) 542-2299 spsi99@telus.net Version 2.015 08-05-2017 Begun 23-06-2008 {pp. 82, 70.2 Kw; 800 KB}