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,
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.
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)
Created from the Publication Database of the Vienna University of Technology.