A note on the symplectic integration of the nonlinear Schrödinger equation

Clemens Heitzinger, Christian Ringhofer

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Numerically solving the nonlinear Schrödinger equation and being able to treat arbitrary space dependent potentials permits many application in the realm of quantum mechanics. The long-term stability of a numerical method and its conservation properties is an important feature since it assures that the underlying physics of the solution are respected and it ensures that the numerical result is correct also for small time spans. In this paper we describe symplectic integrators for the nonlinear Schrödinger equation with arbitrary potentials and perform numerical experiments comparing different approaches and highlighting their respective advantages and disadvantages.

Original languageEnglish (US)
Pages (from-to)33-44
Number of pages12
JournalJournal of Computational Electronics
Volume3
Issue number1
DOIs
StatePublished - 2004

Fingerprint

Symplectic Integration
Nonlinear equations
nonlinear equations
Nonlinear Equations
Symplectic Integrators
Quantum theory
integrators
Convergence of numerical methods
Arbitrary
Quantum Mechanics
Conservation
conservation
quantum mechanics
Numerical methods
Physics
Numerical Methods
Numerical Experiment
Numerical Results
physics
Dependent

Keywords

  • Difference methods
  • Nonlinear Schrödinger equations
  • Symplectic integration

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Atomic and Molecular Physics, and Optics
  • Electronic, Optical and Magnetic Materials
  • Modeling and Simulation

Cite this

A note on the symplectic integration of the nonlinear Schrödinger equation. / Heitzinger, Clemens; Ringhofer, Christian.

In: Journal of Computational Electronics, Vol. 3, No. 1, 2004, p. 33-44.

Research output: Contribution to journalArticle

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