Exponential split operator methods for solving coupled time-dependent Schrödinger equations

Coherent excitation of molecules with laser pulses are usually described by coupled time-dependent linear parabolic partial differential equations, i.e., Schrödinger equations. Numerical solutions of these equations based on splitting (factorization) of the exponential form of the evolution operator or time-dependent propagator are examined for accuracy of amplitude and phase as a function of various unitary splitting schemes.