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Lagrange-mesh calculations and Fourier transform.

Gwendolyn Lacroix1, Claude Semay

  • 1Service de Physique Nucléaire et Subnucléaire, Université de Mons-UMONS, Académie universitaire Wallonie-Bruxelles, Place du Parc 20, B-7000 Mons, Belgium. gwendolyn.lacroix@umons.ac.be

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 9, 2011
PubMed
Summary
This summary is machine-generated.

The Lagrange-mesh method accurately computes quantum eigenvalues and eigenfunctions. This approach simplifies momentum space calculations, enabling precise observable computations from configuration space data.

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Area of Science:

  • Quantum mechanics
  • Computational physics
  • Theoretical chemistry

Background:

  • The Lagrange-mesh method offers high accuracy for solving quantum mechanical problems.
  • Solving two-body quantum equations in configuration space is computationally intensive.
  • Transforming solutions to momentum space often requires separate computational efforts.

Purpose of the Study:

  • To demonstrate the efficiency of the Lagrange-mesh method for quantum eigenvalue and eigenfunction computation.
  • To show that Fourier transforms of eigenfunctions can be accurately obtained in momentum space directly from configuration space calculations.
  • To facilitate the computation of observables in momentum space using existing configuration space results.

Main Methods:

  • Utilizing the Lagrange-mesh method with a Gauss quadrature rule.
  • Expanding eigenfunctions using regularized Lagrange functions.
  • Leveraging the method's properties to perform Fourier transforms and calculate observables.

Main Results:

  • Accurate computation of eigenvalues and eigenfunctions for two-body quantum equations.
  • Efficient calculation of the Fourier transform of eigenfunctions in momentum space.
  • Accurate computation of momentum space observables using only configuration space matrix elements and eigenfunctions.

Conclusions:

  • The Lagrange-mesh method provides a computationally efficient and accurate pathway for solving quantum mechanical problems.
  • The method seamlessly bridges configuration and momentum space calculations, simplifying complex quantum analyses.
  • This approach enhances the practical application of quantum mechanical simulations in various scientific domains.