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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. Schrödinger...

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Classical Mechanics

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Related Experiment Video

Updated: Jun 23, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

How complex is quantum motion?

Giuliano Benenti¹, Giulio Casati

¹CNISM, CNR-INFM, and Center for Nonlinear and Complex Systems, Università degli Studi dell'Insubria, Via Valleggio 11, 22100 Como, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 28, 2009

Summary

This summary is machine-generated.

We introduce a new measure of complexity for quantum systems. This quantum complexity relates to how stable and reversible a quantum system is, unlike in classical mechanics.

Related Experiment Videos

Last Updated: Jun 23, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

Quantum mechanics
Classical mechanics
Dynamical systems theory

Background:

Classical mechanics uses local exponential instability to define system complexity and irreversibility.
Quantum mechanics exhibits strong memory of initial states, contrasting with classical systems.
Understanding quantum system complexity is crucial for quantum information science.

Purpose of the Study:

Introduce a novel notion of complexity for quantum dynamical systems.
Relate this quantum complexity to the stability and reversibility properties of quantum systems.
Provide a framework for quantifying quantum system complexity.

Main Methods:

Developing a theoretical framework for quantum complexity.
Analyzing the relationship between quantum complexity, stability, and reversibility.
Utilizing concepts from dynamical systems theory adapted for quantum mechanics.

Main Results:

A new definition of quantum complexity has been established.
Quantum complexity is shown to be directly linked to system stability and reversibility.
The proposed measure quantifies the 'memory' of initial conditions in quantum systems.

Conclusions:

Quantum systems possess a complexity measure distinct from classical systems.
This quantum complexity offers insights into the unique memory properties of quantum states.
The findings have implications for understanding quantum dynamics and information processing.