  This paper proposes a numerical method for solving time-dependent Schrodinger
equations with finite spectral bandwidth, which applies to both periodic and
non-periodic cases. We introduce the concept of Pulse Width Modulation (PWM),
which is broadly used in classical control engineering, to simulate
time-dependent quantum dynamics by switching between a finite number of
constant Hamiltonians. The switching timings can be programmed to improve the
precision and save computational resources. The effectiveness of the PWM method
is demonstrated by numerical simulations, which shows that it is faster and
more robust than the standard piecewise constant control systems. Moreover, we
also propose the realization of PWM method for potential implementation in
experimental systems.
