On variational approximations in quantum molecular dynamics

DOI10.1090/S0025-5718-04-01685-0zbMath1059.81188MaRDI QIDQ4654020

Christian Lubich

Publication date: 1 March 2005

Published in: Mathematics of Computation (Search for Journal in Brave)

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) Computational methods for problems pertaining to quantum theory (81-08) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Molecular physics (81V55)

Related Items (18)

Various variational approximations of quantum dynamics ⋮ A dynamical low-rank approach to the chemical master equation ⋮ One particle equations for many particle quantum systems: The MCTHDF method ⋮ Quantitative measurement of variational approximations ⋮ The geometry of algorithms using hierarchical tensors ⋮ Low-rank tensor methods for partial differential equations ⋮ A Predictor-Corrector Strategy for Adaptivity in Dynamical Low-Rank Approximations ⋮ Variational approximations using Gaussian ansatz, false instability, and its remedy in nonlinear Schrödinger lattices ⋮ Low rank Tucker-type tensor approximation to classical potentials ⋮ Tensor-product approximation to operators and functions in high dimensions ⋮ An error analysis of the multi-configuration time-dependent Hartree method of quantum dynamics ⋮ Approximation of the time-dependent electronic Schrödinger equation by MCTDHF ⋮ Setting and analysis of the multi-configuration time-dependent Hartree-Fock equations ⋮ Numerical tensor calculus ⋮ Regularity of the multi-configuration time-dependent Hartree approximation in quantum molecular dynamics ⋮ Dynamical low-rank approximation: Applications and numerical experiments ⋮ A literature survey of low-rank tensor approximation techniques ⋮ Separation of scales: dynamical approximations for composite quantum systems*

Uses Software

• MCTDH

Cites Work

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• On the regularity of the electronic Schrödinger equation in Hilbert spaces of mixed derivatives
• Finite element methods (Part 1)
• Adiabatic perturbation theory in quantum dynamics
• An introduction to semiclassical and microlocal analysis

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