Publications in Scientific Journals:
A. Arnold, C. Klein, B. Ujvari:
"WKB-method for the 1D Schrödinger equation in the semi-classical limit: enhanced phase treatment";
BIT Numerical Mathematics,
62
(2022),
22 pages.
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 functions · Higher order WKB-approximation · Asymptotically correct finite difference scheme · Spectral methods
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1007/s10543-021-00868-x
Created from the Publication Database of the Vienna University of Technology.