Phase sensitivity of slow electrons to interactions with weak potentials

The interaction of very slow electrons with weak potentials is investigated in an exactly soluble, one-dimensional quantum mechanical model. Slow electrons are produced by a decelerating ramp potential, as in experimental mirror electron microscopy, so the electrons can interact with a weak field as they slow and reverse direction. Our model provides a wave mechanical interpretation of this turning point region and suggests the possibility of imaging optical fields utilizing the phase of electron matter waves.