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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 nucleus...
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Related Experiment Video

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Quantification of Hydrogen Concentrations in Surface and Interface Layers and Bulk Materials through Depth Profiling with Nuclear Reaction Analysis
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Discrete wave mechanics: The hydrogen atom with angular momentum.

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
|March 1, 1987
PubMed
Summary

This study extends discrete wave mechanics to the hydrogen atom with angular momentum. It predicts a minimum electron-nucleus distance that grows with angular momentum, matching Schrödinger

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Area of Science:

  • Quantum mechanics
  • Atomic physics
  • Computational physics

Background:

  • The hydrogen atom is a fundamental system in quantum mechanics.
  • Previous treatments often focused on zero angular momentum states.
  • Understanding atomic structure requires considering angular momentum effects.

Purpose of the Study:

  • To extend discrete wave mechanics to hydrogen atom states with nonzero angular momentum.
  • To investigate the radial wave functions and their properties.
  • To formulate and solve the relevant finite difference equations.

Main Methods:

  • Discrete wave mechanical treatment applied to the hydrogen atom.
  • Focus on the radial components of wave vectors.
  • Formulation of finite difference equations for numerical solutions.

Main Results:

  • A nonzero minimum distance between the electron and nucleus is predicted.
  • This minimum distance increases with increasing angular momentum.
  • The degeneracy of states with angular momentum matches Schrödinger's equation results.

Conclusions:

  • Discrete wave mechanics can successfully model hydrogen atom states with angular momentum.
  • The predicted minimum distance provides new insights into atomic structure.
  • The method offers an alternative approach to solving quantum mechanical problems.