Stationary Schrödinger equation in the semi-classical limit: WKB-based scheme coupled to a turning point

DOI10.1007/s10092-019-0349-9zbMath1439.34078arXiv1805.10502OpenAlexW2804934956MaRDI QIDQ2302090

Kirian Döpfner, Anton Arnold

Publication date: 25 February 2020

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.10502

zbMATH Keywords

Schrödinger equationasymptotic analysisturning pointsAiry functionparabolic cylinder functionmulti-scale problemhighly oscillatory wave functionshigher-order WKB-approximation

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Stability and convergence of numerical methods for ordinary differential equations (65L20) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Singular perturbations for ordinary differential equations (34E15) Numerical solution of singularly perturbed problems involving ordinary differential equations (65L11)

Related Items

Highly Oscillatory Problems with Time-Dependent Vanishing Frequency ⋮ WKB-based scheme with adaptive step size control for the Schrödinger equation in the highly oscillatory regime ⋮ WKB-method for the 1D Schrödinger equation in the semi-classical limit: enhanced phase treatment

Uses Software

• DLMF

Cites Work

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