Time-Independent Quantum Mechanical Problems

Abstract

The Hamiltonian of the problems considered in Chapters 8–10 depended explicitly upon time. In other words, there was an external parameter of the system whose dependence upon time was fixed and did not alter during the course of the collision. In reactions where colliding systems are ions and atoms, the nuclear separation R is such a parameter. If the energy of the nuclear motion is low and comparable with that of the electronic transitions, R must be included in the list of the dynamical variables of the system, i.e., the nuclear motion must be treated quantally. This approach is definitely required if, for instance, we deal with reactions near thresholds.