PROPERTIES OF THE TRANSITION SUPEROPERATOR

Two different transition superoperators naturally arise in physical th eories. First, there is the abstract transition superoperator that ari ses in the quantum Boltzmann equation and collision cross sections. Se cond, there is a transition superoperator that arises in the theory of spectral line broadening. The latter is parameterized by the frequenc y of the light being observed. At present the standard method of evalu ating the effects of transition superoperators is through the use of t ransition operators. However, the connection between transition supero perators and operators has been the subject of controversy while the d iversity 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 potent ial with explicit calculations for a particular one-dimensional model. In this way the validity of previously presented abstract mathematica l arguments is demonstrated explicitly.