Emergent Mind
High-order WKB-based Method For The 1D Stationary Schrödinger Equation In The Semi-classical Limit
(2310.00963)
Published Oct 2, 2023
in
math.NA
and
cs.NA
Abstract
We consider 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 discuss their efficient numerical integration on coarse grids, but still yielding accurate solutions. The $\mathcal{O}(h2)$ one-step method from [2] is based on an analytic WKB-preprocessing of the equation. Here we extend this method to $\mathcal{O}(h3)$ accuracy.
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