The hyperbolic cross space approximation of electronic wavefunctions

DOI10.1007/s00211-006-0038-xzbMath1116.78007OpenAlexW1967026886MaRDI QIDQ868666

Harry Yserentant

Publication date: 6 March 2007

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-006-0038-x

zbMATH Keywords

Schrödinger equationelectronic wave functionshyerbolic cross space approximation

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) PDEs in connection with quantum mechanics (35Q40) Motion of charged particles (78A35)

Related Items (11)

The Optimization Landscape for Fitting a Rank-2 Tensor with a Rank-1 Tensor ⋮ Sparse grids, adaptivity, and symmetry ⋮ Regularity for eigenfunctions of Schrödinger operators ⋮ Musings on multilinear fitting ⋮ On the mixed regularity of N-body Coulombic wavefunctions ⋮ The mixed regularity of electronic wave functions in fractional order and weighted Sobolev spaces ⋮ Sampling and cubature on sparse grids based on a B-spline quasi-interpolation ⋮ Better Approximations of High Dimensional Smooth Functions by Deep Neural Networks with Rectified Power Units ⋮ \(O(d \log N)\)-quantics approximation of \(N\)-\(d\) tensors in high-dimensional numerical modeling ⋮ Efficient Spectral-Element Methods for the Electronic Schrödinger Equation ⋮ Analytic structure of many-body Coulombic wave functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the regularity of the electronic Schrödinger equation in Hilbert spaces of mixed derivatives
• On the essential spectrum of Schrödinger operators
• Handbook of Numerical Analysis X. Special volume: Computational chemistry.
• Sparse grid spaces for the numerical solution of the electronic Schrödinger equation
• Computational chemistry from the perspective of numerical analysis
• Sparse grids
• Sparse grids for the Schrödinger equation
• From atoms to crystals: a mathematical journey
• BestN-term approximation in electronic structure calculations I. One-electron reduced density matrix
• Bounds for the Discrete Part of the Spectrum of a Semi-Bounded Schrödinger Operator.
• On the computation of the eigenproblems of hydrogen and helium in strong magnetic and electric fields with the sparse grid combination technique
• The efficient computation of certain determinants arising in the treatment of Schrödinger's equations

This page was built for publication: The hyperbolic cross space approximation of electronic wavefunctions