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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.

Atomic Orbitals

Atomic Orbitals

An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.

Quantum Numbers

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.

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...

Atomic Structure

Atomic Structure

The Greek philosopher Democritus proposed that everything on Earth is made up of tiny particles called atomos, Greek for "indivisible," from which the modern term "atom" is derived. In the 19th century, John Dalton proposed the atomic theory that is still largely correct today. He put forth five postulates to explain how atoms made up the world around us. (1) All matter is composed of infinitely small particles or atoms. (2) All atoms of a given element are identical to one...

Atomic Nuclei: Nuclear Spin State Population Distribution

Atomic Nuclei: Nuclear Spin State Population Distribution

Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.

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Updated: Jul 17, 2025

Nanofabrication of Gate-defined GaAs/AlGaAs Lateral Quantum Dots

Nanofabrication of Gate-defined GaAs/AlGaAs Lateral Quantum Dots

Published on: November 1, 2013

Atomically precise vacancy-assembled quantum antidots.

Hanyan Fang¹, Harshitra Mahalingam², Xinzhe Li³

¹Department of Chemistry, National University of Singapore, Singapore, Singapore.

Nature Nanotechnology

|August 31, 2023

Summary

This summary is machine-generated.

Researchers fabricated atomic-scale quantum antidots using a novel bottom-up method. These precisely controlled structures exhibit tunable quantum properties and enhanced robustness for quantum information and photocatalysis applications.

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Silicon Metal-oxide-semiconductor Quantum Dots for Single-electron Pumping

Silicon Metal-oxide-semiconductor Quantum Dots for Single-electron Pumping

Published on: June 3, 2015

Area of Science:

Condensed Matter Physics
Materials Science
Quantum Engineering

Background:

Antidot lattices in 2D systems exhibit unique transport properties and quantum phenomena.
Precise atomic-scale control over antidot size and spacing has been a significant challenge.
Quantum antidots with discrete quantum hole states are crucial for exploring new quantum phenomena.

Purpose of the Study:

To develop an atomically precise bottom-up fabrication method for quantum antidots.
To investigate the quantum properties and tunability of these novel antidots.
To assess the potential of these structures for quantum information and photocatalysis.

Main Methods:

Atomically precise bottom-up fabrication of quantum antidots using thermal-induced assembly of chalcogenide single vacancies in PtTe₂.
Creation of highly ordered single-vacancy lattices with atomic-scale precision.
Characterization of quantum hole states and their tunability through varying vacancy density and doping.

Main Results:

Achieved ultimate downscaling limit of antidot lattices with single-vacancy lattices spaced by a single Te atom.
Demonstrated tunable multilevel quantum hole states with gaps tunable from telecom to far-infrared regimes.
Showcased robustness of quantum hole states against oxygen substitutional doping.

Conclusions:

Single-vacancy-assembled quantum antidots offer unprecedented control and tunability at the atomic scale.
These structures exhibit remarkable robustness, making them ideal for advanced applications.
The developed fabrication method opens new avenues for quantum information processing and photocatalysis.