Showing papers by "Th. Monovasilis published in 2006"
TL;DR: In this article, the Schrodinger equation was transformed into a Hamiltonian canonical equation and the solution of the one-dimensional time-independent Schroffinger equation is considered by exponentially fitted symplectic integrators.
Abstract: The solution of the one-dimensional time-independent Schrodinger equation is considered by exponentially fitted symplectic integrators. The Schrodinger equation is first transformed into a Hamiltonian canonical equation. Numerical results are obtained for the one-dimensional harmonic oscillator and the doubly anharmonic oscillator.
86 citations
01 Jan 2006
TL;DR: In this article, the Schrodinger equation was transformed into a Hamiltonian canonical equation and the solution of the one-dimensional time-independent Schroffinger equation is considered by exponentially fitted symplectic integrators.
Abstract: The solution of the one-dimensional time-independent Schrodinger equation is considered by exponentially fitted symplectic integrators. The Schrodinger equation is first transformed into a Hamiltonian canonical equation. Numerical results are obtained for the one-dimensional harmonic oscillator and the doubly anharmonic oscillator.
78 citations
TL;DR: In this article, the numerical integration of Hamiltonian systems by symplectic and trigonometrically symplectic method is considered and new methods of second and third order are constructed.
26 citations
TL;DR: In this article, the Schrodinger equation is first transformed into a Hamiltonian canonical equation, and then the high-state eigenvalues of the one-dimensional time-independent Schroffinger equation are considered by symplectic integrators.
Abstract: The computation of high-state eigenvalues of the one-dimensional time-independent Schrodinger equation is considered by symplectic integrators. The Schrodinger 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
6 citations