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Related Concept Videos

The Quantum-Mechanical Model of an Atom02:45

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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Related Experiment Video

Updated: Jun 29, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Periodic orbit basis for the quantum baker map.

Leonardo Ermann1, Marcos Saraceno

  • 1Departamento de Física, Comisión Nacional de Energía Atómica, Avenida del Libertador 8250, C1429BNP Buenos Aires, Argentina. ermann@tandar.cnea.gov.ar

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2008
PubMed
Summary
This summary is machine-generated.

Researchers simplified quantum state descriptions using classical periodic orbits from chaotic maps. Including manifold propagation improved this basis, enhancing quantum chaos studies.

Related Experiment Videos

Last Updated: Jun 29, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

  • Quantum mechanics
  • Chaos theory
  • Mathematical physics

Background:

  • Describing quantum eigenstates of chaotic systems is complex.
  • Classical periodic orbits offer insights into quantum chaos.
  • Basis sets are crucial for simplifying quantum mechanical descriptions.

Purpose of the Study:

  • To simplify the description of quantum eigenstates for chaotic maps.
  • To develop an improved basis set using classical periodic orbits.
  • To quantify the quality of the proposed basis set.

Main Methods:

  • Utilizing a basis set derived from classical periodic orbits of a chaotic map.
  • Incorporating short-time propagation along stable and unstable manifolds.
  • Applying the average participation ratio to assess basis set quality.

Main Results:

  • The proposed basis set significantly simplifies the description of quantum eigenstates.
  • Inclusion of manifold propagation refines the basis, analogous to scar functions.
  • The average participation ratio effectively quantifies the basis's quality.

Conclusions:

  • A novel basis set based on classical periodic orbits offers a simplified approach to quantum chaos.
  • The method provides a more efficient way to study quantum eigenstates in chaotic systems.
  • This approach enhances the understanding of quantum-classical correspondence in chaotic dynamics.