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Discrete wave mechanics: An introduction.

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
|August 1, 1986
PubMed
Summary
This summary is machine-generated.

This study introduces discrete wave mechanics for 1D systems, using wave vectors and a new wave vector energy. The approach aligns with relativistic principles and Schrödinger

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Area of Science:

  • Quantum Mechanics
  • Theoretical Physics
  • Computational Physics

Background:

  • Traditional quantum mechanics relies on wave functions.
  • Schrödinger's wave mechanics is a cornerstone of quantum theory.
  • Relativistic effects are crucial for high-energy particles.

Purpose of the Study:

  • To formulate discrete wave mechanics for 1D systems.
  • To introduce wave vectors and wave vector energy as alternatives to wave functions.
  • To explore the compatibility of this new formulation with relativistic quantum mechanics.

Main Methods:

  • Utilizing a simple finite difference equation for discrete wave mechanics.
  • Developing solutions involving wave vectors and a novel "wave vector energy."
  • Analyzing the behavior of the system in the limit as c → ∞ to recover Schrödinger's wave mechanics.

Main Results:

  • The discrete wave mechanics formulation yields solutions with wave vectors and wave vector energy.
  • In the non-relativistic limit (c → ∞), the treatment converges to Schrödinger's wave mechanics.
  • Calculations for free particles and particles in a 1D box show compatibility with relativistic considerations.
  • Wave vectors exhibit properties analogous to particles and antiparticles, with identical probability distributions and zero total energy.

Conclusions:

  • Discrete wave mechanics provides a viable framework for 1D quantum systems.
  • The concept of wave vectors and wave vector energy offers new insights into particle behavior.
  • The formulation demonstrates a significant connection to relativistic physics, particularly in its treatment of particle-antiparticle duality.