PROPERTIES OF THE TRANSITION SUPEROPERATOR

Two different transition superoperators naturally arise in physical theories. First, there is the abstract transition superoperator that arises in the quantum Boltzmann equation and collision cross sections. Second, there is a transition superoperator that arises in the theory of spectral line broadening. The latter is parameterized by the frequency of the light being observed. At present the standard method of evaluating the effects of transition superoperators is through the use of transition operators. However, the connection between transition superoperators and operators has been the subject of controversy while the diversity of transition superoperators and operators can be confusing. This paper reviews the basic definitions and methods of relating these quantities, exemplifying these properties by using a separable potential with explicit calculations for a particular one-dimensional model. In this way the validity of previously presented abstract mathematical arguments is demonstrated explicitly.