Quantum two-particle scattering in fuzzy phase space

Abstract

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