Zernike Polynomials Applied to Schrondinger's Equation

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SUMMARY

Zernike Polynomials have not been directly applied to Schrödinger's Equation as solutions for wavefunctions, primarily due to their restriction to two-dimensional disk geometries and their lack of status as solutions to the equation itself. Despite these limitations, Zernike Polynomials are recognized for their utility in optics and may have potential applications in specific numerical quantum mechanics problems. Further exploration into their integration with quantum mechanics could yield valuable insights.

PREREQUISITES
  • Understanding of Schrödinger's Equation in quantum mechanics
  • Familiarity with Zernike Polynomials and their applications in optics
  • Knowledge of wavefunction properties and constraints
  • Basic principles of numerical methods in quantum mechanics
NEXT STEPS
  • Research the application of Zernike Polynomials in numerical quantum mechanics problems
  • Study the mathematical properties of Zernike Polynomials in detail
  • Explore alternative polynomial solutions to Schrödinger's Equation
  • Investigate the implications of dimensional constraints on wavefunctions
USEFUL FOR

Quantum physicists, optical engineers, and researchers exploring advanced numerical methods in quantum mechanics will benefit from this discussion.

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There are two obstacles:
1. The Zernike polynomials only apply to wavefunctions restricted to a two dimensional disk which is a rather special problem.
2. The Zernike polynomial seem not to be solutions of a Schroedinger equation.

This does not exclude that they may be usefull in some special numerical qm problems.
 

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