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Related Concept Videos

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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Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

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In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must...
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The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

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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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Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

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NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of...
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Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

948
Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
948
The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

42.0K
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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Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
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Spin-Bounded Correlations: Rotation Boxes Within and Beyond Quantum Theory.

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Quantum theory allows the most general rotational correlations for spins 0, 1/2, and 1. Beyond-quantum resources with spin 3/2 outperform quantum resources in a metrological game.

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Area of Science:

  • Foundations of Quantum Mechanics
  • Quantum Information Theory
  • Mathematical Physics

Background:

  • Investigates how detector click probabilities relate to spatial rotations in physical theories.
  • Introduces 'rotation boxes' as a mathematical tool analogous to non-local boxes.
  • Explores the fundamental constraints imposed by spacetime geometry on quantum theory.

Purpose of the Study:

  • To mathematically analyze rotational correlations in detector click probabilities across various physical theories.
  • To characterize the limits of quantum correlations and explore potential beyond-quantum phenomena.
  • To establish connections between spacetime physics and semi-device-independent quantum information.

Main Methods:

  • Detailed mathematical analysis using the concept of 'rotation boxes'.
  • Proving Tsirelson-type inequalities for higher spins.
  • Developing an efficient outer semidefinite programming (SDP) approximation for general spin-J correlations.

Main Results:

  • Quantum theory exhibits the most general rotational correlations for spins 0, 1/2, and 1.
  • A metrological game demonstrates beyond-quantum resources with spin 3/2 surpassing quantum counterparts.
  • Fundamental results include convex characterization of spin-1 correlations and Tsirelson-type inequalities for spin 3/2 and higher.

Conclusions:

  • The study illuminates how spatial constraints shape quantum theory.
  • Establishes a link between semi-device-independent quantum information and spacetime physics.
  • Demonstrates applications in randomness generation, Bell correlations, and multipartite Bell witnesses.