Related Experiment Video
Updated: Jun 29, 2026

Quantification of Hydrogen Concentrations in Surface and Interface Layers and Bulk Materials through Depth Profiling with Nuclear Reaction Analysis
Published on: March 29, 2016
Confined hydrogen atom by the Lagrange-mesh method: energies, mean radii, and dynamic polarizabilities
1Physique Quantique, C.P. 165/82, Université Libre de Bruxelles, B 1050 Brussels, Belgium. dbaye@ulb.ac.be
Abstract:
The Lagrange-mesh method is an approximate variational calculation which resembles a mesh calculation because of the use of a Gauss quadrature. The hydrogen atom confined in a sphere is studied with Lagrange-Legendre basis functions vanishing at the center and surface of the sphere. For various confinement radii, accurate energies and mean radii are obtained with small numbers of mesh points, as well as dynamic dipole polarizabilities. The wave functions satisfy the cusp condition with 11-digit accuracy.
Related Concept Videos
The Energies of Atomic Orbitals
Molecular Orbital Theory II
Atomic Orbitals
Hydrogen Bonds
Hydrogen Bonds
Potential Due to a Polarized Object
