A case study on the reliability of multiphase WKB approximation for the one-dimensional Schrödinger equation

Laurent Gosse (1)

1 IAC - Istituto per le Applicazioni del Calcolo "Mauro Picone"

We present a short overview of high-frequency asymptotics for the 1D Schrödinger equation while emphasizing the computational aspects. We show that presumably different techniques like stationary phase methods, WKB or Wigner analysis give esssentially the same macroscopic behaviour. Moment systems and K-branch entropy solutions are introduced in order to derive well-suited numerical methods. Finally, we display some computations supporting these ideas on a classical example.

Mots clés: Schrodinger equation; semiclassical limit; WKB approximation; Markov moment inversion; Wigner measure.; Wigner measure

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Laurent Gosse. A case study on the reliability of multiphase WKB approximation for the one-dimensional Schrödinger equation. Stéphane Cordier et al. Numerical methods for hyperbolic and kinetic problems: CEMRACS 2003, European Mathematical Society, pp.131-141, 2005. ⟨hal-00426866⟩