Contributions to Books:
A. Arnold, C. Klein, B. Ujvari:
"WKB-method for the 1D Schrödinger equation in the semi-classical limit: enhanced phase treatment";
in: "ASC Report 19/2018",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
Wien,
2018,
ISBN: 978-3-902627-11-7,
1
- 17.
English abstract:
This paper is concerned with the efficient numerical computation of solutions to the 1D stationary Schrödinger equation in the semiclassical limit in the highly oscillatory regime. A previous approach to this problem based on explicitly incorporating the leading terms of the WKB approximation is enhanced in two ways: first a refined error analysis for the method is presented for a not explicitly known WKB phase, and secondly the phase and its derivatives will be computed with spectral methods. The efficiency of the approach is illustrated for several examples
Keywords:
Uniformly accurate scheme, Schrödinger equation, highly oscillating wave func-tions, higher order WKB-approximation, asymptotically correct finite difference scheme, spectral methods
Electronic version of the publication:
http://www.asc.tuwien.ac.at/preprint/2018/asc19x2018.pdf
Created from the Publication Database of the Vienna University of Technology.