WKB-method for the 1D Schr\"odinger equation in the semi-classical limit: enhanced phase treatment
Numerical Analysis
2019-11-05 v2 Numerical Analysis
Abstract
This paper is concerned with the efficient numerical computation of solutions to the 1D stationary Schr\"odinger 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
Cite
@article{arxiv.1808.01887,
title = {WKB-method for the 1D Schr\"odinger equation in the semi-classical limit: enhanced phase treatment},
author = {A. Arnold and C. Klein. B. Ujvari},
journal= {arXiv preprint arXiv:1808.01887},
year = {2019}
}