Propagator calculations for time dependent Dirac delta potentials and corresponding two state models

Abstract

Time dependent Dirac delta potential is an interesting problem in quantum mechanics due to its applications in various fields. In this paper we have worked on this problem for two different models. We have derived the propagator for scattering problems in presence of a Dirac delta potential. Here strength of the potential is a function of time i.e.f(t). We have devised a mathematical method to solve this problem using Green's function method. We have also solved the corresponding two state model and find exact results. Our results are purely analytical and we have reported exact expressions of ψ(x′,t) in all cases.