We describe a computational method for simulating time-dependent quantum mechanical systems interacting with external fields. In this method, the Schrödinger equation is solved by expanding the wave function in the basis set of the unperturbed Hamiltonian. The expansion yields a set of coupled ordinary differential equations for the expansion coefficients. This coupled channel method can be applied to many time-dependent problems. We apply the coupled channel method to a particle in a box interacting with a laser pulse. We show that if only two states are involved, the method leads naturally to the solutions for Rabi flopping, and that the system exhibits Rabi flopping behavior even with realistic, nonmonochromatic laser pulses. We also discuss instances where simulations could improve the understanding or address misconceptions of beginning students in quantum mechanics.