Spatial dependence of weakly localized single-photon wave packets

Using the theory of generalized imprimitivities for the description of weakly localized single-photon states, the spatial dependence of the photodetection of such states is calculated and an $x^{\mathrm{-}7}$ falloff is found. A general technique for determining the falloff of densities associated with weakly localized states is given and in particular the same spatial dependence is found for the falloff of energy density in agreement with the previous work of Amrein.