WIAS Preprint No. 1313, (2008)

A review of transparent and artificial boundary conditions techniques for linear and nonlinear Schrödinger equations


  • Antoine, Xavier
  • Arnold, Anton
  • Besse, Christophe
  • Ehrhardt, Matthias
  • Schädle, Achim

2010 Mathematics Subject Classification

  • 65M12 35Q40 45K05

2008 Physics and Astronomy Classification Scheme

  • 02.70.Bf 31.15.Fx


  • Schrödinger equation, transparent boundary conditions, discrete convolution, unbounded domain, finite difference schemes, finite elements




In this review article we discuss different techniques to solve numerically the time-dependent Schrödinger equation on unbounded domains. We present in detail the most recent approaches and describe briefly alternative ideas pointing out the relations between these works. We conclude with several numerical examples from different application areas to compare the presented techniques. We mainly focus on the one-dimensional problem but also touch upon the situation in two space dimensions and the cubic nonlinear case.

Appeared in

  • Commun. Comput. Phys., 4 (2008) pp. 729--796.

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