Transition time in a two-state system involving similar and non-similar potential energy curves coupled by δ-potential

The study of the transition time has been remained unexplored in the multistate problems in quantum mechanics. There is hardly a method available to calculate that quantity. In this work, we have proposed a simple method of calculating transition time and study the characteristics of it by observing its dependency on coupling strength and the energy of the system, etc. We have adopted the method of tunneling time estimation to implement the method for transition time in a two-stage model, where states are coupled by a δ-function. An explicit dependence on both the potential energy curves as well as on the coupling strength has been observed. For a simple two constant potentials energy states, we also noticed that the coupling potential appears as almost being transparent and nearly being opaque to the incident wave, depending upon its energy. Our calculated transition time non-monotonically depends on the incident energy and coupling strength.