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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.

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.

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.

Atomic Radii and Effective Nuclear Charge

Atomic Radii and Effective Nuclear Charge

The elements in groups of the periodic table exhibit similar chemical behavior. This similarity occurs because the members of a group have the same number and distribution of electrons in their valence shells.

Atomic Structure

Atomic Structure

Atomic Mass

Atomic Mass

Atoms — and the protons, neutrons, and electrons that compose them — are extremely small. For example, a carbon atom weighs less than 2 × 10−23 g. When describing the properties of tiny objects such as atoms, we use appropriately small units of measure, such as the atomic mass unit (amu). The amu was originally defined based on hydrogen, the lightest element, then later in terms of oxygen. Since 1961, it has been defined with regard to the most abundant isotope of carbon, atoms of which...

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Related Experiment Video

Updated: Feb 6, 2026

Simulating Imaging of Large Scale Radio Arrays on the Lunar Surface

Simulating Imaging of Large Scale Radio Arrays on the Lunar Surface

Published on: July 30, 2020

Large-scale analogue quantum simulation using atom dot arrays.

M B Donnelly^1,2, Y Chung³, R Garreis³

¹Silicon Quantum Computing Pty. Ltd., UNSW Sydney, Sydney, New South Wales, Australia. matthew.donnelly@sqc.com.au.

|February 4, 2026

Summary

This summary is machine-generated.

Researchers developed a novel quantum simulator using 15,000 atom-based quantum dots. This system precisely simulates strongly interacting, low-temperature physics, advancing quantum materials research.

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Last Updated: Feb 6, 2026

Simulating Imaging of Large Scale Radio Arrays on the Lunar Surface

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Published on: July 30, 2020

Production and Targeting of Monovalent Quantum Dots

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Compact Quantum Dots for Single-molecule Imaging

Published on: October 9, 2012

Area of Science:

Quantum simulation
Condensed matter physics
Quantum computing

Background:

Analogue quantum systems are crucial for simulating complex quantum phenomena.
Existing platforms struggle with large-scale, strongly interacting fermionic systems at low temperatures.
Electronic correlations in materials are key but challenging to simulate accurately.

Purpose of the Study:

To introduce a new, large-scale analogue quantum simulator.
To enable the simulation of strongly interacting, low-temperature physics.
To overcome limitations of current quantum simulation platforms.

Main Methods:

Utilized large-scale 2D arrays of precision-engineered atom-based quantum dots (15,000 sites).
Engineered independent and precise control over on-site interaction (U) and tunneling (t).
Performed magneto-transport measurements to probe electronic properties.

Main Results:

Observed a metal-insulator transition on a 2D square lattice.
Demonstrated precise control over interaction and tunneling parameters.
Indicated an insulating state driven by Mott-Hubbard/Anderson physics with correlated electron signatures.

Conclusions:

The new platform offers a unique capability for simulating quantum materials on arbitrary 2D lattices.
Enables exploration of quantum magnetism, interacting topological quantum matter, and unconventional superconductivity.
Advances the pursuit of practical quantum advantage through analogue quantum simulation.