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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.

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The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...

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Related Experiment Video

Updated: Jan 24, 2026

Analysis of Contact Interfaces for Single GaN Nanowire Devices

Analysis of Contact Interfaces for Single GaN Nanowire Devices

Published on: November 15, 2013

Modeling Atomic-Scale Electrical Contact Quality Across Two-Dimensional Interfaces.

Aisheng Song¹, Ruoyu Shi¹, Hongliang Lu^2,3

¹State Key Laboratory of Tribology , Tsinghua University , Beijing 100084 , China.

|May 16, 2019

Summary

This summary is machine-generated.

Researchers developed a new model to measure electrical contact conductance at the atomic level. This breakthrough links atomic structure to conductance, improving understanding of electronic transport across interfaces like graphene on ruthenium.

Keywords:

Two-dimensional materials ab initio calculations atomic resolution imaging electrical contacts heterostructure real-space model

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Last Updated: Jan 24, 2026

Analysis of Contact Interfaces for Single GaN Nanowire Devices

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Published on: November 15, 2013

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Published on: September 17, 2017

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Published on: October 4, 2016

Area of Science:

Surface Science and Nanotechnology
Condensed Matter Physics
Materials Science

Background:

Electrical conduction across contacting interfaces is often limited by physical isolation and weak interactions.
Previous models correlating contact conductance with contact area (e.g., Landauer's theory, Richardson formulation) lacked atomistic detail.
A quantitative model directly linking interfacial atomistic structure to contact conductance was missing.

Purpose of the Study:

To establish a quantitative, real-space model connecting atomic-scale contact quality to local interfacial atomistic structure.
To measure atomic-scale local electrical contact conductance at graphene/Ru(0001) interfaces.
To investigate the twist angle-dependent interlayer conductance in misoriented graphene layers.

Main Methods:

Utilized atomically resolved conductive atomic force microscopy (c-AFM) to measure local electrical contact conductance.
Focused on measuring local electrical contact conductance, not local electronic surface states.
Defined atomic-scale contact quality based on carrier tunneling probability along interatomic pathways.

Main Results:

Established a direct relationship between atomic-scale contact quality and local interfacial atomistic structure.
Unraveled the atomic-level spatial modulation of contact conductance at the graphene/Ru(0001) interface.
Observed and quantified twist angle-dependent interlayer conductance between misoriented graphene layers.

Conclusions:

The developed real-space model provides unprecedented insight into atomic-level control of interfacial electrical conductance.
This work bridges the gap between macroscopic conductance measurements and fundamental atomic interactions.
Findings are crucial for designing advanced electronic devices utilizing 2D materials and van der Waals heterostructures.