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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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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 one, the...
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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 the...
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Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
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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.
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All atomic particles possess an intrinsic angular momentum, or 'spin'. Electrons, protons, and neutrons each have a spin value of ½, although protons and neutrons in nuclei may have higher half-integer spins owing to energetic factors.
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Gradient Echo Quantum Memory in Warm Atomic Vapor
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Quantum Rydberg Central Spin Model.

Yuto Ashida1,2, Tao Shi3, Richard Schmidt4,5

  • 1Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.

Physical Review Letters
|November 26, 2019
PubMed
Summary
This summary is machine-generated.

We studied Rydberg impurities interacting with ultracold atoms, revealing new quantum phenomena like spin oscillations and spectrum renormalization not seen in traditional impurity models.

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Area of Science:

  • Quantum physics
  • Atomic physics
  • Condensed matter physics

Background:

  • Rydberg impurities in ultracold atomic gases present complex quantum phenomena.
  • Existing models struggle to capture the interplay between electron spin dynamics and atomic motion.

Purpose of the Study:

  • To investigate the dynamics of a Rydberg impurity interacting with a cloud of ultracold bosonic atoms.
  • To develop a theoretical framework for understanding novel quantum impurity problems.

Main Methods:

  • Employed a new variational method combining impurity-decoupling transformation and a Gaussian ansatz.
  • Analyzed the interplay of Rydberg-electron spin dynamics and atomic bath behavior.

Main Results:

  • Observed interaction-induced renormalization of the absorption spectrum, defying simple explanations.
  • Discovered long-lasting oscillations in the Rydberg-electron spin.
  • Identified unique features not present in traditional impurity problems.

Conclusions:

  • The studied system offers a new paradigm for quantum impurity physics.
  • Findings have implications for atomic physics and quantum chemistry involving electron excitation and spinful quantum baths.