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

On the Foundations of Quantum Mechanics

Richard Joseph Oldani

Published Mar 4, 2026• 0 citations
Publisher

Abstract

Matrix mechanics describes the spectral emissions of hydrogen gas, but quantum mechanics concerns the emission and absorption of radiation by a single atom. To obtain the spectral emissions of a single hydrogen atom we reformulate matrix mechanics by introducing thermal energy in infinitesimal increments and registering the spectral lines one by one until a complete spectrum is obtained. Wave mechanics is reformulated from a conservative to a non-conservative system by linking the output of matrix mechanics to the input of wave mechanics. To describe the gradual increase and decrease of energy by a quantum system we integrate between two specific endpoints, the atomic orbitals, and two specific times, the period τ, which are the conditions necessary for Hamilton’s principle. The Lagrangian method is shown to be superior for analyzing quantum theory because it describes quantum systems relativistically as evolutions in time.

DOI
10.20944/preprints202510.0504.v4

Related papers

On the Foundations of Quantum Mechanics

Richard Joseph Oldani

Matrix mechanics describes the spectral emissions of hydrogen gas, but quantum mechanics concerns the emission and absorption of radiation by a single atom. To obtain the spectral emissions of a single hydrogen atom we introduce thermal energy in infinitesimal increments registering the spectral lines one by one until a complete spectrum is obtained. We describe the gradual increase of the internal quantum mechanical energy in a non-conservative system by integrating between two specific endpoints, the atomic orbitals, and two specific times, the period τ, which are the conditions necessary for Hamilton’s principle. Wave mechanics is shown to be limited to conservative systems. A complete quantum mechanics is formulated using energy-time conjugate variables as the time integral of a Lagrangian independently of Hamiltonian formulations that use position-momentum conjugate variables.

•Feb 18, 2026•0 citations

On the Foundations of Quantum Mechanics

Richard Joseph Oldani

Matrix mechanics describes the spectral emissions of hydrogen gas, but quantum mechanics concerns the emission and absorption of radiation by a single atom. To obtain the spectral emissions of a single hydrogen atom we introduce thermal energy in infinitesimal increments registering the spectral lines one by one until a complete spectrum is obtained. We describe the gradual increase of the internal quantum mechanical energy by integrating between two specific endpoints, the atomic orbitals, and two specific times, the period τ, which are the conditions necessary for Hamilton’s principle. Continuous time is thereby introduced to quantum mechanics during energy absorption by means of a Lagrangian formulation using energy-time conjugate variables, independently of Hamiltonian formulations that use position-momentum conjugate variables.

•Dec 2, 2025•0 citations

Quantum Mechanics and the Arrow of Time

Richard Joseph Oldani

We reformulate matrix mechanics by incrementally heating a single hydrogen atom in order to derive the complete, diagonalized Hamiltonian matrix. The spectral lines and transition probabilities cannot be generated by reversing time thereby demonstrating asymmetry. Experimental evidence in support of the theoretical model is obtained from experiments performed with the simplest quantum system, an electron cyclotron. Wave mechanics is also reformulated by altering the original Schrödinger equation describing a time symmetric, conservative system to a system of two independent equations describing a time asymmetric, non-conservative system.

•Mar 20, 2026•0 citations

Quantum Mechanics and the Arrow of Time

Richard Joseph Oldani

We reformulate matrix mechanics by incrementally heating a single hydrogen atom in order to derive the complete, diagonalized Hamiltonian matrix. The spectral lines and transition probabilities cannot be generated by reversing time thereby demonstrating asymmetry. Experimental evidence in support of the theoretical model is obtained from experiments performed with the simplest quantum system, an electron cyclotron. Wave mechanics is also reformulated by altering the original Schrödinger equation describing a time symmetric, conservative system to a system of two independent equations describing a time asymmetric, non-conservative system.

•May 26, 2026•0 citations

A Complete Quantum Mechanics

Richard Joseph Oldani

We hypothesize that quantum mechanics is incomplete because it does not take into consideration the absorption of energy by quantum systems as described by matrix mechanics. To be complete quantum mechanics must include both matrix and wave mechanics, and due to the conservation of energy the first (absorption) must be carried out to completion before the second one (emission) can begin. The combined model of matrix and wave mechanics integrates naturally with Einstein’s use of independent coordinate systems K and K’ to describe the absorption and emission of radiation. All subsequent mathematical models are versions of this physical model.

Qeios•Oct 3, 2024•0 citations

A Complete Quantum Mechanics That Is Also Visualizable

Richard Joseph Oldani

We hypothesize that quantum mechanics is incomplete because it does not take into consideration the absorption of energy by quantum systems as described by matrix mechanics. To be complete quantum mechanics must include both matrix and wave mechanics, and due to the conservation of energy the first (absorption) must be carried out to completion before the second one (emission) can begin. The combined model of matrix and wave mechanics integrates naturally with Einstein’s use of independent coordinate systems K and K’ to describe the absorption and emission of radiation. All subsequent mathematical models are versions of this physical model.

Qeios•Nov 5, 2024•0 citations
Matrix mechanics describes the spectral emissions of hydrogen gas, but quantum mechanics concerns the emission and absorption of radiation by a single atom. To obtain the spectral emissions of a single hydrogen atom we reformulate matrix mechanics by introducing thermal energy in infinitesimal increments and registering the spectral lines one by one until a complete spectrum is obtained. Wave mechanics is reformulated from a conservative to a non-conservative system by linking the output of matrix mechanics to the input of wave mechanics. To describe the gradual increase and decrease of energy by a quantum system we integrate between two specific endpoints, the atomic orbitals, and two specific times, the period τ, which are the conditions necessary for Hamilton’s principle. The Lagrangian method is shown to be superior for analyzing quantum theory because it describes quantum systems relativistically as evolutions in time.
Matrix mechanics describes the spectral emissions of hydrogen gas, but quantum mechanics concerns the emission and absorption of radiation by a single atom. To obtain the spectral emissions of a single hydrogen atom we introduce thermal energy in infinitesimal increments registering the spectral lines one by one until a complete spectrum is obtained. We describe the gradual increase of the internal quantum mechanical energy in a non-conservative system by integrating between two specific endpoints, the atomic orbitals, and two specific times, the period τ, which are the conditions necessary for Hamilton’s principle. Wave mechanics is shown to be limited to conservative systems. A complete quantum mechanics is formulated using energy-time conjugate variables as the time integral of a Lagrangian independently of Hamiltonian formulations that use position-momentum conjugate variables.
Matrix mechanics describes the spectral emissions of hydrogen gas, but quantum mechanics concerns the emission and absorption of radiation by a single atom. To obtain the spectral emissions of a single hydrogen atom we introduce thermal energy in infinitesimal increments registering the spectral lines one by one until a complete spectrum is obtained. We describe the gradual increase of the internal quantum mechanical energy by integrating between two specific endpoints, the atomic orbitals, and two specific times, the period τ, which are the conditions necessary for Hamilton’s principle. Continuous time is thereby introduced to quantum mechanics during energy absorption by means of a Lagrangian formulation using energy-time conjugate variables, independently of Hamiltonian formulations that use position-momentum conjugate variables.
We reformulate matrix mechanics by incrementally heating a single hydrogen atom in order to derive the complete, diagonalized Hamiltonian matrix. The spectral lines and transition probabilities cannot be generated by reversing time thereby demonstrating asymmetry. Experimental evidence in support of the theoretical model is obtained from experiments performed with the simplest quantum system, an electron cyclotron. Wave mechanics is also reformulated by altering the original Schrödinger equation describing a time symmetric, conservative system to a system of two independent equations describing a time asymmetric, non-conservative system.
We reformulate matrix mechanics by incrementally heating a single hydrogen atom in order to derive the complete, diagonalized Hamiltonian matrix. The spectral lines and transition probabilities cannot be generated by reversing time thereby demonstrating asymmetry. Experimental evidence in support of the theoretical model is obtained from experiments performed with the simplest quantum system, an electron cyclotron. Wave mechanics is also reformulated by altering the original Schrödinger equation describing a time symmetric, conservative system to a system of two independent equations describing a time asymmetric, non-conservative system.
We hypothesize that quantum mechanics is incomplete because it does not take into consideration the absorption of energy by quantum systems as described by matrix mechanics. To be complete quantum mechanics must include both matrix and wave mechanics, and due to the conservation of energy the first (absorption) must be carried out to completion before the second one (emission) can begin. The combined model of matrix and wave mechanics integrates naturally with Einstein’s use of independent coordinate systems K and K’ to describe the absorption and emission of radiation. All subsequent mathematical models are versions of this physical model.
We hypothesize that quantum mechanics is incomplete because it does not take into consideration the absorption of energy by quantum systems as described by matrix mechanics. To be complete quantum mechanics must include both matrix and wave mechanics, and due to the conservation of energy the first (absorption) must be carried out to completion before the second one (emission) can begin. The combined model of matrix and wave mechanics integrates naturally with Einstein’s use of independent coordinate systems K and K’ to describe the absorption and emission of radiation. All subsequent mathematical models are versions of this physical model.