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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 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...

The Pauli Exclusion Principle

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:

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...

The Uncertainty Principle

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Fermi Level Dynamics

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The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
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Related Experiment Video

Updated: Jul 24, 2025

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

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Published on: August 2, 2019

Quantum Chaos in the Extended Dicke Model.

¹CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, SI-2000 Maribor, Slovenia.

Entropy (Basel, Switzerland)

|July 8, 2023

Summary

We investigated quantum chaos in interacting atoms coupled to a bosonic field. Atomic interactions amplify chaos, impacting spectral statistics more than eigenstate structure.

Keywords:

eigenstate structure extended Dicke model quantum chaos spectral statistics

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Area of Science:

Quantum physics
Quantum many-body systems
Quantum chaos

Background:

The Dicke model describes interacting quantum systems but lacks atom-atom interactions.
Understanding quantum chaos is crucial for complex quantum systems.

Purpose of the Study:

To investigate quantum chaotic signatures in the extended Dicke model with atom-atom interactions.
To analyze the influence of interatomic interactions on chaos indicators.
To compare the effects of atomic interactions on spectral statistics and eigenstate structure.

Main Methods:

Analysis of energy spectral statistics.
Examination of eigenstate structures.
Investigation of eigenvalue-based and eigenstate-based chaos indicators.

Main Results:

Quantum signatures of chaos were identified in the extended Dicke model.
Interatomic interactions were found to amplify the integrability-to-chaos transition.
Atomic interactions have a stronger impact on spectral statistics than on eigenstate structure.

Conclusions:

The extended Dicke model exhibits distinct quantum chaotic behaviors influenced by interatomic interactions.
The findings provide insights into the role of interactions in driving quantum systems towards chaos.