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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 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...

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 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:

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...

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Related Experiment Video

Updated: Nov 14, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Shaping quantum photonic states using free electrons.

A Ben Hayun¹, O Reinhardt¹, J Nemirovsky¹

¹Department of Electrical Engineering and Solid State Institute, Technion, Israel Institute of Technology, Haifa 32000, Israel.

Science Advances

|March 11, 2021

Summary

This summary is machine-generated.

Researchers propose generating quantum light via free-electron interactions, a novel method using electron microscopes to create unique light states like squeezed and entangled light.

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Area of Science:

Quantum optics
Free-electron physics
Photonics

Background:

Generating quantum light with unique properties like squeezing and entanglement is a key goal in quantum optics.
Free-electron interactions are widely used for classical light generation.
Recent advances in electron microscopy show quantum free-electron interactions with light in photonic cavities.

Purpose of the Study:

To propose a novel method for generating quantum light using free-electron interactions.
To explore the use of electron microscopes as platforms for shaping quantum light states.
To theoretically demonstrate the creation of specific quantum light states.

Main Methods:

Utilizing electron energy combs to perform photon displacement operations.
Developing theoretical models for consecutive electron-cavity interactions.
Leveraging quantum free-electron interactions within photonic cavities.

Main Results:

Demonstrated the creation of displaced-Fock and displaced-squeezed states of light.
Developed a theoretical framework for generating any target Fock state through sequential electron-cavity interactions.
Showcased the potential of electron microscopes for quantum light generation.

Conclusions:

Free-electron interactions offer a promising new avenue for generating tailored quantum light.
Electron microscopes can be engineered to precisely control quantum states of light.
This approach may lead to novel light statistics and correlations for future quantum technologies.