High-order WKB-based Method For The 1D Stationary Schrödinger Equation In The Semi-classical Limit

2023/10/02 by Anton Arnold, Arnold, Anton, Jannis Körner +1
Physics and Astronomy · #Gyrotron and Vacuum Electronics Research #Cold Atom Physics and Bose-Einstein Condensates #Quantum, superfluid, helium dynamics

paper · pdf · doi:10.48550/arxiv.2310.00963

Abstract

We consider initial value problems for ε² φ''+a(x) φ=0 in the highly oscillatory regime, i.e., with a(x)>0 and 0<ε≪ 1. We discuss their efficient numerical integration on coarse grids, but still yielding accurate solutions. The O(h²) one-step method from [2] is based on an analytic WKB-preprocessing of the equation. Here we extend this method to O(h³) accuracy.

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