Accurate Chebyshev wave packet method for solving molecular dynamics processes with laser pulses of long durations

Abstract The development of accurate and efficient numerical methods for solving the Schrödinger equation with explicitly time-dependent potentials involving long-duration laser pulses is challenging, where the short time propagation method usually is inefficient. Within the ( t , t ′ ) formalism, the explicitly time-dependent Hamiltonians can be rewritten as time-independent Floquet-type Hamiltonians, and thus, numerical methods with high accuracy could be developed conveniently. In this work, numerical methods based on Chebyshev polynomials expansion in the order domain are proposed to solve the Schrödinger equation involving long-duration laser interactions in ( t , t ′ ) form. With a one-dimensional forced Morse oscillator model, the methods are shown to be globally convergent and highly accurate over long propagation intervals. These methods are further employed to study the Stark-induced adiabatic Raman passage for exciting HD molecule from v = 0 , J = 0 state to v = 1 , J = 0 state, which is important in a molecular crossed beam experiment.