Exact time-dependent solutions for a double-well model

Lie algebraic techniques are used to obtain exact solutions of the time-dependent Schrödinger equation for a model double-well potential with an applied, time-dependent, dipole field. The model potential consists of harmonic potentials in x > 0 and x < 0 with an interface region spanning the origin and the theory of the matching of the wavefunctions for the three different regions is examined in detail. The time-dependent solutions are shown to give rise to two independent types of charge transfer arising from a positional change in the wave packet due to the applied field and the change of shape of the wave packet due to interference effects.