Gauss-Hermite wave packet dynamics: convergence of the spectral and pseudo-spectral approximation. (English) Zbl 1183.65111
Authors’ summary: The time-dependent linear Schrödinger equation for nuclei on the whole space is semidiscretized using Hermite and Gauss-Hermite basis functions. These are well suited, on the one hand, for the conservation properties of the numerical solution and, on the other hand, for their remarkable approximation properties. We investigate theoretically and numerically the convergence of the spectral and pseudo-spectral Gauss-Hermite semidiscretization schemes.
Reviewer: Jiří Vaníček (Praha)
MSC:
65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |
65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
35Q40 | PDEs in connection with quantum mechanics |
81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |