Lagrange-mesh calculations and Fourier transform

Journal Article · Thu Sep 15 00:00:00 EDT 2011 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)

DOI:https://doi.org/10.1103/PHYSREVE.84.036705· OSTI ID:21611757

Lacroix, Gwendolyn; Semay, Claude ^[1]

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1. Service de Physique Nucleaire et Subnucleaire, Universite de Mons-UMONS, Academie universitaire Wallonie-Bruxelles, Place du Parc 20, B-7000 Mons (Belgium)

The Lagrange-mesh method is a very accurate procedure for computing eigenvalues and eigenfunctions of a two-body quantum equation written in the configuration space. Using a Gauss quadrature rule, the method only requires the evaluation of the potential at some mesh points. The eigenfunctions are expanded in terms of regularized Lagrange functions, which vanish at all mesh points except one. Using the peculiarities of the method, it is shown that the Fourier transform of the eigenfunctions, computed in the configuration space, can easily be obtained with good accuracy in the physical domain of the momentum space. Also, observables in this space can easily be computed with good accuracy only using matrix elements and eigenfunctions computed in the configuration space.

• OSTI ID: 21611757
• Journal Information: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Vol. 84, Issue 3; Other Information: DOI: 10.1103/PhysRevE.84.036705; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1539-3755
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICAL METHODS AND COMPUTING
ACCURACY
CONFIGURATION
EIGENFUNCTIONS
EIGENVALUES
EQUATIONS
EVALUATION
FOURIER TRANSFORMATION
MATHEMATICAL SPACE
MATRIX ELEMENTS
QUADRATURES
TWO-BODY PROBLEM
FUNCTIONS
INTEGRAL TRANSFORMATIONS
MANY-BODY PROBLEM
SPACE
TRANSFORMATIONS