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The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.

The Bohr Model

The Bohr Model

Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded by lighter and even tinier electrons continually moving about the nucleus was well established. This picture was called the planetary model since it pictured the atom as a miniature “solar system” with the electrons orbiting the nucleus like planets orbiting the sun. The simplest atom is hydrogen, consisting of a single proton as...

Electron Orbital Model

Electron Orbital Model

Orbitals are the areas outside of the atomic nucleus where electrons are most likely to reside. They are characterized by different energy levels, shapes, and three-dimensional orientations. The location of electrons is described most generally by a shell or principal energy level, then by a subshell within each shell, and finally, by individual orbitals found within the subshells.
The first shell is closest to the nucleus, and it has only one subshell with a single spherical orbital called the...

The Uncertainty Principle

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...

Electronic Structure of Atoms

Electronic Structure of Atoms

An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum...

The de Broglie Wavelength

The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...

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Related Experiment Video

Updated: Oct 3, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

A local-realistic model for quantum theory.

Paul Raymond-Robichaud¹

¹ISI Foundation, Turin, Italy.

Proceedings. Mathematical, Physical, and Engineering Sciences

|February 14, 2022

Summary

This summary is machine-generated.

This study rigorously defines local realism and demonstrates that the universal wave function is insufficient for a complete description of local reality. A local-realistic model for quantum theory is successfully constructed.

Keywords:

Everett local-realism no-signalling quantum theory universal wave function

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Last Updated: Oct 3, 2025

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Area of Science:

Quantum mechanics
Foundations of physics
Quantum information theory

Background:

The interpretation of quantum mechanics remains a subject of debate.
Local realism, a cornerstone of classical intuition, faces challenges from quantum phenomena.
The completeness of the universal wave function as a description of reality is questioned.

Purpose of the Study:

To provide a rigorous mathematical definition of local realism.
To investigate the compatibility of the universal wave function with local realism.
To develop a local-realistic model that can reproduce quantum theory predictions.

Main Methods:

Formal derivation of local realism axioms.
Mathematical analysis of the universal wave function's properties.
Construction of a novel theoretical framework for a local-realistic model.

Main Results:

A precise definition of local realism is established.
It is proven that the universal wave function cannot fully describe local reality.
A consistent local-realistic model for quantum theory is developed.

Conclusions:

The universal wave function is not a complete description of local reality.
Quantum theory can be potentially explained within a local-realistic framework.
This work opens new avenues for understanding the foundations of quantum mechanics.