Quantum two-particle scattering in fuzzy phase space
- 1 September 1976
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 17 (9), 1673-1681
- https://doi.org/10.1063/1.523115
Abstract
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.Keywords
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