Stationary approaches for solving the Schrödinger equation with time-dependent Hamiltonians

Abstract

Accurate and efficient computational schemes are utilized for solving the Schrödinger equation with time-dependent Hamiltonians. These schemes, based on an extended Hilbert space in which time is treated like a space coordinate, allow essentially all of the computational strategies for stationary problems to be equally applicable to explicitly time-dependent problems. In particular, variational principles, the discrete variable representation in time, the fast Fourier transform in time, the recursive residue generation method (RRGM), and the Chebyshev propagator can be employed. Some of these methods are implemented and tested for a rigid rotor interacting with various laser pulses. The fast exponential convergence with respect to the number of time grid points is illustrated, which accounts for the high accuracy of the methods (limited only by the precision of computer), a feature which is hardly achievable by other methods.