From Quantum to Classical Molecular Dynamics: Reduced Models and Numerical AnalysisEuropean Mathematical Society, 2008 - 144 pages Quantum dynamics of molecules poses a variety of computational challenges that are presently at the forefront of research efforts in numerical analysis in a number of application areas: high-dimensional partial differential equations, multiple scales, highly oscillatory solutions, and geometric structures such as symplecticity and reversibility that are favourably preserved in discretizations. This text addresses such problems in quantum mechanics from the viewpoint of numerical analysis, illustrating them to a large extent on intermediate models between the Schrodinger equation of full many-body quantum dynamics and the Newtonian equations of classical molecular dynamics. The fruitful interplay between quantum dynamics and numerical analysis is emphasized. |
Table des matières
1 | 7 |
1 | 14 |
Numerical Methods for the TimeDependent Schrödinger Equation | 63 |
Numerical Methods for NonLinear Reduced Models | 105 |
SemiClassical Dynamics Using Hagedorn Wave Packets | 123 |
| 137 | |
Expressions et termes fréquents
algorithm approximation manifold Chebyshev coefficients collocation complex compute condition consider coordinates denote derivative differential equations discretization e-it eigenfunctions eigenvalue electronic equations of motion error bound exponential formula Fourier transform free Schrödinger equation Galerkin method Gaussian wave packets Hagedorn Hamiltonian Hartree method Hartree-Fock method Hermite functions Hermitian matrix Hilbert space hyperbolic cross initial data inner product integral kinetic energy L2 norm Lanczos method Lemma Lubich matrix exponential mean-field multi-configuration multi-indices nuclei numerical obtain orthonormal parameters particles polynomial Proof quadratic potential quadrature quantum mechanics result satisfy Schrödinger equation Schrödinger equation 0.1 Sect self-adjoint operator single-particle functions solution sparse grid splitting method Strang splitting symmetric symplectic tangent space tensor products Theorem time-dependent Hartree time-dependent Schrödinger equation time-dependent variational principle variational approximation variational principle variational splitting vector wave function wave packet yields მს