The concepts of configuration and momentum representation space for state vectors are generalized to that of fuzzy-phase-space representation spaces L2(Γs), 0<s<∞, which are interpolated in between these two standard representations. It is shown that the wavepacket in L2(Γs) displays the familiar evanescence property from any region Ks × Ms in the fuzzy phase space Γs if that region is bounded in its configuration part Ks; also, that the probability of detecting the system in Ks × Ms has a finite asymptotic time limit if Ks is a (fuzzy) cone. For scattering states the existence of free states that are asymptotic in Γs is established, and a formula for differential cross section in Γs is derived.