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Related Concept Videos

The Bohr Model02:18

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Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded by lighter and even tinier electrons continually moving about the nucleus was well established. This picture was called the planetary model since it pictured the atom as a miniature “solar system” with the electrons orbiting the nucleus like planets orbiting the sun. The simplest atom is hydrogen, consisting of a single proton as...
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In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
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Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
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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...
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The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
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The probability of having two carbon-13 atoms next to each other is negligible because of the low natural abundance of carbon-13. Consequently, peak splitting due to carbon-carbon spin-spin coupling is not observed in spectra. However, protons up to three sigma bonds away split the carbon signal according to the n+1 rule, resulting in complicated spectra.
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Related Experiment Video

Updated: May 4, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Sub-Planck structure in phase space and its relevance for quantum decoherence.

W H Zurek1

  • 1Theory Division, T-6, MS B288, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA. whz@LANL.gov

Nature
|August 17, 2001
PubMed
Summary

Heisenberg

Area of Science:

  • Quantum mechanics
  • Quantum chaos
  • Quantum information

Background:

  • Heisenberg's uncertainty principle traditionally implies sub-Planck scales are insignificant.
  • Classical chaos amplifies quantum effects, driving systems into non-local states.
  • Understanding sub-Planck scale significance is crucial for quantum system analysis.

Purpose of the Study:

  • To challenge the assumption that sub-Planck scales are irrelevant.
  • To demonstrate the physical significance of sub-Planck structures in quantum systems.
  • To investigate the role of sub-Planck scales in decoherence and quantum measurement sensitivity.

Main Methods:

  • Theoretical analysis of non-local quantum superpositions ('Schrödinger's cat' states).
  • Investigation of phase space structures within volumes larger than Planck's constant.

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  • Modeling quantum chaotic systems using chaotic scattering principles.

    • Main Results:

    • Non-local quantum superpositions develop significant structure at sub-Planck scales (a = hbar / 2A).
    • This structure formation is accelerated in quantum chaotic systems.
    • The sub-Planck scale 'a' dictates system sensitivity to perturbations.

    Conclusions:

    • Sub-Planck scales are physically significant and not negligible.
    • The scale 'a' governs environmental interactions, including decoherence and pointer state selection.
    • This scale is vital for understanding quantum meter sensitivity limits.