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 assymptotic symplecticness is introduced. A family of assymptotically symplectic methods of order p is developed, and applied in the construction of methods of 5th and 7th order. Numerical results are obtained for the one-dimentional harmonic oscillator and the hydrogen atom.
