Symplectic integrators for the numerical solution of the Schrödinger equation

Authors:
Z. Kalogiratou;Th. Monovasilis;T. E. Simos
Affiliations:
Department of International Trade, Technological Educational Institute of Western Macedonia at Kastoria, P.O. Box 30, GR-521 00, Kastoria, Greece;Department of International Trade, Technological Educational Institute of Western Macedonia at Kastoria, P.O. Box 30, GR-521 00, Kastoria, Greece;Department of Computer Science and Technology, Faculty of Science and Technology, University of Peloponnese, University Campus, GR-221 00 Tripolis, Greece
Venue:
Journal of Computational and Applied Mathematics - Special issue: Selected papers from the conference on computational and mathematical methods for science and engineering (CMMSE-2002) Alicante University, Spain, 20-25 september 2002
Year:
2003

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Abstract

The solution of the one-dimensional time-independent Schrödinger equation is considered by symplectic integrators. The Schrödinger equation is first transformed into a Hamiltonian canonical equation. The concept of asymptotic symplecticness is introduced and asymptotically symplectic methods of order up to 3 are developed. Numerical results are obtained for the one-dimensional harmonic oscillator, the hydrogen atom and the one dimensional double-well anharmonic oscillator.