HIGHER-ORDER UNITARY INTEGRATORS FOR THE SCHRODINGER-EQUATION

For classical Hamiltonian dynamics, much progress has recently been made in manifestly symplectic integrators. In this work some of these integrators will be generalized to the Schrodinger equation. There they correspond to algorithms which preserve unitarity and time reversal invariance exactly. In particular, we apply them to the one-dimensional harmonic and anharmonic oscillators. The accuracies of the three different algorithms are compared.