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The Quantum-Mechanical Model of an Atom02:45

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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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Atomic force microscopy (AFM) is a type of scanning probe microscopy that can analyze topographic details of various specimens like ceramics, glass, polymers, and biological samples. AFM offers over 1000 times more resolution than the optical imaging system. Images generated from AFM are three-dimensional surface profiles, offering an advantage over the flat, two-dimensional images from other imaging techniques.
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Updated: Oct 11, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Quantum-coherent nanoscience.

Andreas J Heinrich1,2, William D Oliver3,4, Lieven M K Vandersypen5

  • 1Center for Quantum Nanoscience (QNS), Institute for Basic Science, Seoul, Korea. heinrich.andreas@qns.science.

Nature Nanotechnology
|November 30, 2021
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Summary
This summary is machine-generated.

Quantum-coherent nanoscience merges quantum physics with nanoscale systems. This review explores quantum coherence applications in charge, spin, motion, and photon control for future quantum technologies.

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Area of Science:

  • Physics, chemistry, and engineering
  • Quantum science and technology
  • Nanoscience

Background:

  • Nanoscience has impacted physics, chemistry, and engineering for 30 years.
  • Quantum science and technology is a cross-disciplinary field with commercial potential.
  • Quantum coherence, key to quantum information, has been underutilized in nanoscience.

Purpose of the Study:

  • To describe fundamental principles and applications of quantum coherence in nanoscale systems.
  • To introduce the field of quantum-coherent nanoscience.
  • To highlight challenges and opportunities at the intersection of nanoscience and quantum operations.

Main Methods:

  • Reviewing fundamental principles of quantum coherence.
  • Analyzing applications in nanoscale systems.
  • Structuring the review by controllable degrees of freedom (charge, spin, motion, photons).

Main Results:

  • Nanoscience and quantum technology are converging.
  • Quantum coherence can be controlled in various nanoscale degrees of freedom.
  • The integration offers new avenues for quantum information, communication, and sensing.

Conclusions:

  • Quantum-coherent nanoscience is an emerging field with significant potential.
  • Further research can unlock advanced quantum technologies.
  • Merging nanoscience with coherent quantum operations presents unique challenges and opportunities.