Transition time estimation for δ-function coupling in two state problem: An analytically solvable model

• DOI: 10.1016/j.cplett.2021.138436
• Publication Date: 2021-02-18T07:32:43Z
• Authors: Mayank Vashistha; Chinmoy Samanta; Aniruddha Chakrab...
• Keywords: Quantum Physics; 0103 physical sciences; FOS: Physical sciences; Quantum Physics (quant-ph); 01 natural sciences

We propose a simple method to calculate transition time in a two-state scattering problem, where two constant potentials are coupled by a delta function potential $V_{12}=V_{21}=k_0 ��(x)$. The exact analytical expression for the time of transition $��$ is derived. We notice $��$ explicitly depends on the second state's potential energy along with the incident energy and coupling strength. We also observe from the derived expression of $��$ that depending on the initial energy, the coupling potential could behave like a transparent or opaque medium to the incident wave in a single state equivalent description.