Numerical approximation of quadratic observables of Schrödinger-type equations in the semi-classical limit. (English) Zbl 0928.65109
The Wigner-transform techniques are applied to the analysis of difference methods for Schrödinger-type equations in the case of a small Planck constant. In this way, the authors are able to obtain sharp conditions on the spatial-temporal grid which guarantee convergence for average values of observables as the Planck constant lends to zero. Numerical sample computations and interpretations of the theory are given.
Reviewer: T.C.Mohan (Madras)
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 65Z05 | Applications to the sciences |
