The general wavefunction for a particle under uniform force

We present a simple approach for finding the general solution of the time-dependent Schro ̈dingerequationforaparticlemovingundertheactionofauniformforce.Fromsuchageneral solution we derive the eigenfunctions of the energy as well as those of the momentum. Next we obtain the propagator and show that the time evolution of an arbitrarily chosen initial wavefunction is described by a Fresnel transformation. This establishes a useful link with optical phenomena and allows us to link the case of a particle moving under a uniform force to that of the free particle.