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Computation of the eigenvalues of the one‐dimensional Schrödinger equation by symplectic methods
Author(s) -
Kalogiratou Z.,
Monovasilis Th.,
Simos T. E.
Publication year - 2005
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.20816
Subject(s) - symplectic geometry , eigenvalues and eigenvectors , anharmonicity , symplectic integrator , morse potential , schrödinger equation , harmonic oscillator , hamiltonian (control theory) , mathematics , mathematical physics , variational integrator , computation , mathematical analysis , physics , quantum mechanics , integrator , symplectic manifold , mathematical optimization , voltage , algorithm
The computation of high‐state eigenvalues of the one‐dimensional time‐independent Schrödinger equation is considered by symplectic integrators. The Schrödinger equation is first transformed into a Hamiltonian canonical equation. Yoshida‐type symplectic integrators are used as well as symplectic integrators based on the Magnus expansion. Numerical results are obtained for a wide range of eigenstates of the one‐dimensional harmonic oscillator, the doubly anharmonic oscillator, and the Morse potential. The eigenvalues found by the symplectic methods are compared with the eigenvalues produced by Numerov‐type methods. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006