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Discrete wave mechanics: The hydrogen atom with angular momentum
1Department of Chemistry, B-017, University of California at San Diego, La Jolla, CA 92093.
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
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.
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