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Quantum Numbers02:43

Quantum Numbers

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It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
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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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The polar coordinate system offers an alternative to the Cartesian coordinate system for specifying points in a plane, using a distance and an angle instead of x and y coordinates. This system is particularly advantageous in situations involving circular or rotational symmetry, such as in physics or engineering problems involving waves, oscillations, or orbital paths.Defining Polar CoordinatesIn polar coordinates, a point is represented as P(r, ��), where r is the radial distance...
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Polarity of the Cytoskeleton01:18

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The intrinsic polarity of cells can be primarily attributed to two factors- i) the asymmetric accumulation of mobile components such are regulatory molecules and subcellular components across the cell and ii) the orientation of polar cytoskeletal filaments that make up the cytoskeletal networks, specifically microfilaments, and microtubules arranged along the axis of polarity. Interactions between the cytoskeletal filaments are crucial for the establishment and maintenance of the polar nature...
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Related Experiment Video

Updated: Feb 14, 2026

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

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Quantum-rotor-induced polarization.

Benno Meier1

  • 1School of Chemistry, University of Southampton, Southampton, UK.

Magnetic Resonance in Chemistry : MRC
|February 21, 2018
PubMed
Summary
This summary is machine-generated.

Quantum-rotor-induced polarization, similar to para-hydrogen-induced polarization, uses rotational interactions to create hyperpolarized spin order. This review explores conditions and experimental results for methyl and water-in-fullerene rotors.

Keywords:
hyperpolarizationmethylnuclear spin conversionquantum-rotor-induced polarizationspin isomerismwater

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Area of Science:

  • Quantum physics
  • Spin chemistry
  • Materials science

Background:

  • Quantum-rotor-induced polarization (QRIP) is linked to para-hydrogen-induced polarization (PHIP).
  • Both phenomena leverage rotational interactions and the Pauli principle.
  • The symmetry of the rotational ground state determines the nuclear spin state symmetry.

Purpose of the Study:

  • To review the preconditions for QRIP.
  • To examine QRIP in 1D methyl rotors and asymmetric H217O@C60 rotors.
  • To present experimental findings for these systems.

Main Methods:

  • Discussion of theoretical preconditions for QRIP.
  • Analysis of hetero-nuclear cross-relaxation mechanisms.
  • Presentation of experimental data for methyl and H217O@C60 rotors.

Main Results:

  • Identified key conditions enabling QRIP in specific molecular systems.
  • Demonstrated QRIP generation via hetero-nuclear cross-relaxation.
  • Presented experimental validation for both methyl and H217O@C60 rotors.

Conclusions:

  • QRIP is a viable method for generating hyperpolarized spin order.
  • The symmetry of rotational states is crucial for QRIP.
  • Experimental evidence supports QRIP in diverse rotor systems.