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Related Concept Videos

Correspondence Bias01:17

Correspondence Bias

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Correspondence bias, also referred to as the fundamental attribution error, describes the tendency to attribute another person’s behavior to internal characteristics rather than situational influences. This cognitive bias leads individuals to overlook external factors that may be influencing actions, thereby fostering potentially inaccurate assessments of others’ intentions and dispositions.Empirical Evidence for Correspondence BiasResearch has consistently demonstrated the...
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Theory of Attribution I: Correspondent Inference Theory01:15

Theory of Attribution I: Correspondent Inference Theory

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Correspondent inference theory, proposed by Jones and Davis in 1965, seeks to explain how individuals infer stable personality traits from observed behaviors. It suggests that people attribute actions to underlying dispositions rather than external circumstances, particularly when the behavior appears intentional and socially significant.Voluntary Behavior and Dispositional AttributionAccording to this theory, individuals are more likely to attribute behavior to personal traits when it appears...
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Ionic Crystal Structures02:42

Ionic Crystal Structures

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Ionic crystals consist of two or more different kinds of ions that usually have different sizes. The packing of these ions into a crystal structure is more complex than the packing of metal atoms that are the same size.
Most monatomic ions behave as charged spheres, and their attraction for ions of opposite charge is the same in every direction. Consequently, stable structures for ionic compounds result (1) when ions of one charge are surrounded by as many ions as possible of the opposite...
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Crystal Growth: Principles of Crystallization01:25

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Crystallization is a phase transformation process in which crystals are precipitated from a supersaturated solution or formed from other sources. During crystallization, atoms or molecules arrange themselves into a well-defined, rigid crystal lattice to minimize energy.
Initiating crystallization involves manipulating the concentration of the solute and the temperature of the solution. Since crystal growth occurs when the ratio of concentration and solubility of the solute in the solvent...
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Crystal Field Theory - Octahedral Complexes02:58

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Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
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Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

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Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
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Applying X-ray Imaging Crystal Spectroscopy for Use as a High Temperature Plasma Diagnostic
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Schrödinger Correspondence Applied to Crystals.

Eric J Heller1,2, Donghwan Kim1

  • 1Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.

The Journal of Physical Chemistry. A
|March 21, 2019
PubMed
Summary

Schrödinger

Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Solid State Physics

Background:

  • The Schrödinger Correspondence Principle (1926) links quantum and classical mechanics for harmonic oscillators.
  • Extending this principle to N-dimensional systems offers a classical approach to quantum problems in harmonic solids.
  • Understanding phonons, pseudomomentum, and center-of-mass momentum is crucial for applying this principle.

Purpose of the Study:

  • To clarify concepts like phonons and pseudomomentum for applying the correspondence principle.
  • To introduce the concept of the antiphonon in atomic systems.
  • To analyze quantum behavior in harmonic solids using classical methods via the correspondence principle.

Main Methods:

  • Extension of the Schrödinger Correspondence Principle to N-dimensional harmonic oscillators.

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  • Conceptual clarification of phonons, pseudomomentum, and center-of-mass momentum.
  • Introduction of the antiphonon concept through atomic line and ring models.
  • Classical analysis of quantum harmonic solid behavior under a Mössbauer-like kick.

    • Main Results:

    • The correspondence principle provides an intuitive classical framework for quantum harmonic solids.
    • The concept of the antiphonon is introduced and illustrated.
    • Classical analysis successfully predicted and simulation verified the formation of an antiphonon.

    Conclusions:

    • The Schrödinger Correspondence Principle is a powerful tool for simplifying quantum mechanical problems in harmonic solids.
    • The antiphonon concept offers new insights into the dynamics of atomic systems.
    • Classical analysis, aided by the correspondence principle, effectively models quantum phenomena like antiphonon formation.