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Discrete wave mechanics: Multidimensional systems.

F T Wall1

  • 1Department of Chemistry, B-017, University of California at San Diego, La Jolla, CA 92093.

Proceedings of the National Academy of Sciences of the United States of America
|May 1, 1987
PubMed
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This study extends discrete wave mechanics to multiple dimensions, revealing energy as a product of parameters and enabling easier variable separation. Group velocity in higher dimensions is also analyzed.

Area of Science:

  • Physics
  • Quantum Mechanics
  • Wave Mechanics

Background:

  • Previous work established one-dimensional discrete wave mechanics.
  • Momentum considerations are crucial for understanding particle behavior.

Purpose of the Study:

  • Extend discrete wave mechanics to two or more dimensions.
  • Investigate the impact of particle motion on mass and inter-directional motion.
  • Analyze energy parameter behavior and variable separation in higher dimensions.
  • Discuss group velocity components in multi-dimensional systems.

Main Methods:

  • Explicit momentum considerations were applied.
  • The effect of particle motion on mass was analyzed.
  • The principal energy parameter was factored.

Related Experiment Videos

  • Wave vector expressions were factored.
  • Group velocity components were derived for higher dimensions.

    • Main Results:

    • The overall energy parameter in higher dimensions is a product, not a sum.
    • Separation of variables is achieved by factoring the energy parameter and wave vector.
    • Wave vector energies remain additive.
    • Group velocity components for higher-dimensional systems were discussed.

    Conclusions:

    • The multi-dimensional discrete wave mechanics framework offers a new perspective on energy and variable separation.
    • This approach simplifies analysis by factoring key parameters.
    • The findings provide a basis for further exploration of complex wave phenomena.