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Related Experiment Videos

Locality principle in wave mechanics.

W Kohn1, A Yaniv

  • 1Department of Physics, University of California at San Diego, La Jolla, California 92093.

Proceedings of the National Academy of Sciences of the United States of America
|November 1, 1978
PubMed
Summary
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This study demonstrates a locality principle for quantum particles. The local density of states depends primarily on nearby potential, supporting localized calculation methods.

Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Computational chemistry

Background:

  • The Schrödinger equation describes wave-mechanical particles.
  • Understanding the locality of physical properties in extended systems is crucial.
  • Local methods are widely used in calculations but require theoretical justification.

Purpose of the Study:

  • To prove a locality principle for wave-mechanical particles.
  • To investigate the dependence of the local density of states on the potential.
  • To provide theoretical support for local calculation methods.

Main Methods:

  • The study utilizes the Schrödinger equation.
  • Laplace transform of the local density of states, rho(r,beta), is analyzed.
  • The dependence of rho(r,beta) on the potential V(r') is mathematically derived.

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Main Results:

  • rho(r,beta) depends significantly only on the potential V(r') at nearby points r'.
  • The influence of distant potential changes on rho(r,beta) decays in a Gaussian manner.
  • A clear mathematical relationship between local potential and the local density of states is established.

Conclusions:

  • The findings support a locality principle in quantum systems.
  • This principle explains the localized nature of physical properties in extended systems.
  • The results validate the use of various local methods in computational physics and chemistry.