2012/03/31 by Gwendolyn Lacroix, G. Lacroix, Claude Semay +3 · 8 citations
Mathematics · Physics and Astronomy · #Applied mathematics #Atomic and Molecular Physics #Boundary value problem #Cold Atom Physics and Bose-Einstein Condensates #Computer science #Configuration space #Diagonal #Eigenfunction #Eigenvalues and eigenvectors #Gaussian #Gaussian quadrature #Geometry #Mathematical analysis #Mathematics #Nyström method #Physics #Position and momentum space #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Space (punctuation) #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1103/physreve.86.026705
published in Physical Review E 86(2), 026705 (American Physical Society) · Extended version
arxiv created 2012/05/29 · openalex publication_date 2012/08/08 · arxiv updated 2012/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Lagrange-mesh method is a powerful method to solve eigenequations written in configuration space. It is very easy to implement and very accurate. Using a Gauss quadrature rule, the method requires only 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. It is shown that this method can be adapted to solve eigenequations written in momentum space, keeping the convenience and the accuracy of the original technique. In particular, the kinetic operator is a diagonal matrix. Observables and wave functions in both configuration space and momentum space can also be easily computed with good accuracy using only eigenfunctions computed in the momentum space. The method is tested with Gaussian and Yukawa potentials, requiring, respectively, a small and a large mesh to reach convergence. Corresponding wave functions in both spaces are compared with each other using the Fourier transform.