THE SOLUTION OF THE TIME-DEPENDENT SCHRODINGER-EQUATION BY THE (T,T')-METHOD - THE USE OF GLOBAL POLYNOMIAL PROPAGATORS FOR TIME-DEPENDENT HAMILTONIANS

Using the (t,t') method as introduced in Ref. 1 [J. Chem. Phys. 99, 4590 (1993)] computational techniques which originally were developed for time independent Hamiltonians can be used for propagating an initial state for explicitly time dependent Hamiltonians. The present paper presents a time dependent integrator of the Schrodinger equation based on a Chebychev expansion, of the operator U(x,t',t(0)-->t), and the Fourier pseudospectral method for calculating spatial derivatives [(partial derivative(2)/partial derivative x(2)),(partial derivative/partial derivative t')]. Illustrative numerical examples for harmonic and Morse oscillators interacting with CW and short pulsed laser fields are given.