Trigonometrically and Exponentially fitted Symplectic Methods of third order for the Numerical Integration of the Schrödinger Equation†

Abstract

The solution of the one-dimensional time-independent Schrödinger equation is considered by trigonometrically and exponentially fitted symplectic integrators. The Schrödinger equation is first transformed into a Hamiltonian canonical equation. Numerical results are obtained for the one-dimensional harmonic oscillator and the exponential potential. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)