POSITION-MOMENTUM ENTROPIC UNCERTAINTY RELATION AND COMPLEMENTARITY IN SINGLE-SLIT AND DOUBLE-SLIT EXPERIMENTS

The exact analytical values of the position and momentum information e ntropies are calculated for the single-slit and double-slit diffractio n experiments. In both cases, the product of the exponentials of the e ntropies is strictly greater than the lower bound pi e (h) over bar gi ven by the optimal entropic uncertainty relation for position and mome ntum, which implies that the single-slit and double-slit configuration s are not minimum-uncertainty states. The results obtained show that t he position-momentum entropic uncertainty relation provides a rigorous quantitative expression for the uncertainty principle in these experi ments, unlike the Heisenberg inequality for standard deviations. Howev er, it is also shown that, in the double-slit experiment, wave-particl e duality cannot be derived from the entropic uncertainty relation. [S 1050-2947(98)01202-5].