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Zbl 1027.65171
Kalogiratou, Z.; Monovasilis, Th.; Simos, T.E.
Symplectic integrators for the numerical solution of the Schrödinger equation. (English)
[J] J. Comput. Appl. Math. 158, No.1, 83-92 (2003). ISSN 0377-0427

Summary: 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.

MSC 2000:: *65P10 Hamiltonian systems including symplectic integrators
37M15 Symplectic integrators

Keywords: Schrödinger equation; symplectic integrators; Hamiltonian canonical equation; asymptotically symplectic methods; numerical results; harmonic oscillator; hydrogen atom

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