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Related Concept Videos

The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

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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 Bohr Model02:18

The Bohr Model

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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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Electron Orbital Model01:18

Electron Orbital Model

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Orbitals are the areas outside of the atomic nucleus where electrons are most likely to reside. They are characterized by different energy levels, shapes, and three-dimensional orientations. The location of electrons is described most generally by a shell or principal energy level, then by a subshell within each shell, and finally, by individual orbitals found within the subshells.
The first shell is closest to the nucleus, and it has only one subshell with a single spherical orbital called the...
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The de Broglie Wavelength02:32

The de Broglie Wavelength

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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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Structure of Benzene: Molecular Orbital Model01:18

Structure of Benzene: Molecular Orbital Model

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According to the molecular orbital (MO) model, benzene has a planar structure with a regular hexagon of six sp2 hybridized carbons. As shown in Figure 1, each carbon is bonded to three other atoms with C–C–C and H–C–C bond angles of 120°. The C–H bond length is 109 pm, and the C–C bond length is 139 pm which is midway between the single bond length of sp3 hybridized carbons (154 pm) and sp2 hybridized carbons (133 pm).
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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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Related Experiment Video

Updated: Mar 26, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Generation and Coherent Control of Pulsed Quantum Frequency Combs

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Quantum Stoner-Wohlfarth Model.

Takuya Hatomura1, Bernard Barbara2,3, Seiji Miyashita1,4

  • 1Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-Ku, Tokyo 113-0033, Japan.

Physical Review Letters
|February 6, 2016
PubMed
Summary

We studied quantum magnets in magnetic fields. Increasing spin size slows state changes, causing quantum phase transitions and revealing new insights into metastability and magnetization dynamics.

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Area of Science:

  • Quantum magnetism
  • Condensed matter physics
  • Theoretical physics

Background:

  • The Stoner-Wohlfarth model describes classical magnetic systems.
  • Understanding quantum effects in magnetism is crucial for developing new magnetic materials and devices.
  • The behavior of magnetic systems under external fields is a fundamental area of research.

Purpose of the Study:

  • To investigate the quantum mechanical behavior of an easy-axis magnet in a tilted magnetic field.
  • To explore the influence of spin size (S) on magnetic transitions in a sweeping longitudinal field.
  • To analyze the dynamics of quantum phase transitions and metastability in magnetic systems.

Main Methods:

  • Theoretical analysis of the quantum mechanical Stoner-Wohlfarth model.
  • Computational simulations to study the system's behavior.
  • Investigation as a function of spin size S.
  • Analysis of sweeping longitudinal magnetic fields.

Main Results:

  • The sweeping field-induced adiabatic change of states slows down with increasing spin size S.
  • A dynamical quantum phase transition is observed beyond the classical Stoner-Wohlfarth transition.
  • Metastability collapse is linked to critical phenomena and Landau-Zener tunneling gaps.
  • A beating in the amplitude of magnetization (spin-length fidelity) is discovered post-transition.
  • The beating period is analytically confirmed to originate from a novel quantum phase factor.

Conclusions:

  • Quantum effects significantly alter magnetic behavior compared to classical models.
  • Spin size is a critical parameter influencing the dynamics of quantum phase transitions.
  • The findings provide a new framework for understanding metastability and quantum tunneling in magnetic systems.
  • The discovery of magnetization beating offers fresh perspectives on quantum phase factors and spin dynamics.