Article révisé par les pairs
| Résumé : | We analyse the quantum mechanical collision operator for three incident free particles from the point of view of transport theory. Starting from the Liouville-von Neumann equation for the density matrix, in the form introduced previously by Prigogine and coworkers, we obtain the generalization to quantum systems of the well known Choh-Uhlenbeck result for classical genuine triple collisions. This expression, written in terms of the Heisenberg operators of motion exp[-iHt] for two and three particles, is free of the divergence difficulties occurring in standard collision theory when the limits of a large system and of long times are taken in order to define a three particle transition probability. We also discuss the connection of this result with the Lippman-Schwinger theory and show that the scattering operator for three incident particles is not expressible as the square of a scattering matrix, like in the two particle problem. © 1957. |
