Exact solution to the curve crossing problems of two linear diabatic potentials by transfer matrix method

Abstract

In the present work we have reported a simple exact analytical solution to the curve crossing problem of two linear diabatic potentials by transfer matrix method. Our problem assumes the crossing of two linear diabatic potentials which are coupled to each other by an arbitrary coupling (in contrast to linear potentials in the vicinity of crossing points) and for numerical calculation purposes this arbitrary coupling is taken as Gaussian coupling which is further expressed as a collection of Dirac delta functions. Further we calculated the transition probability from one diabatic potential to another by the use of this method.