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Related Experiment Videos

Nystrom plus correction method for solving bound-state equations in momentum space.

A Tang1, J W Norbury

  • 1Physics Department, University of Wisconsin-Milwaukee, P. O. Box 413, Milwaukee, Wisconsin 53201, USA. atang@uwm.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 21, 2001
PubMed
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This study introduces a novel Nystrom method for solving the momentum-space Schrödinger equation. It enhances eigenvalue accuracy for linear potentials, outperforming traditional basis function methods.

Area of Science:

  • Quantum mechanics
  • Computational physics

Background:

  • Solving the momentum-space Schrödinger equation is crucial for understanding quantum systems.
  • Linear potentials present challenges for traditional numerical methods.
  • Existing methods like basis function approaches have limitations in accuracy.

Purpose of the Study:

  • To present an improved numerical method for solving the momentum-space Schrödinger equation with linear potentials.
  • To enhance the accuracy of eigenvalue calculations for singular potentials.
  • To demonstrate the method's applicability to relativistic equations.

Main Methods:

  • Transformation of the Lande-subtracted momentum-space integral equation into a matrix equation using the Nystrom method.
  • Calculation and correction of numerical errors to improve approximate eigenvalues.

Related Experiment Videos

  • Application to the relativistic Thompson equation.

    • Main Results:

    • The Nystrom method provides approximate eigenvalues for linear potentials.
    • Error correction significantly improves the accuracy of these eigenvalues.
    • The developed method yields more accurate eigenvalues compared to the basis function method.
    • The method is effective for relativistic equations like the Thompson equation.

    Conclusions:

    • The Nystrom method, with error correction, offers a more accurate approach to solving the momentum-space Schrödinger equation for linear potentials.
    • This technique provides a valuable alternative to basis function methods.
    • The method's success with the Thompson equation suggests broader applicability in relativistic quantum mechanics.