Optimally truncated WKB approximation for the highly oscillatory stationary 1D Schrödinger equation
(2310.00955)Abstract
We discuss the numerical solution of initial value problems for $\varepsilon2\,\varphi''+a(x)\,\varphi=0$ in the highly oscillatory regime, i.e., with $a(x)>0$ and $0<\varepsilon\ll 1$. We analyze and implement an approximate solution based on the well-known WKB-ansatz. The resulting approximation error is of magnitude $\mathcal{O}(\varepsilon{N})$ where $N$ refers to the truncation order of the underlying asymptotic series. When the optimal truncation order $N_{opt}$ is chosen, the error behaves like $\mathcal{O}(\varepsilon{-2}\exp(-c\varepsilon{-1}))$ with some $c>0$.
We're not able to analyze this paper right now due to high demand.
Please check back later (sorry!).
Generate a summary of this paper on our Pro plan:
We ran into a problem analyzing this paper.