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

• URL: http://arxiv.org/abs/2010.04497v1
• Date: Fri, 9 Oct 2020 10:56:47 GMT
• Title: Transition time estimation for $\delta$-function coupling in two state problem: An analytically solvable model
• Authors: Mayank Vashistha, Chinmoy Samanta, Aniruddha Chakraborty
• Abstract summary: We propose a simple method to calculate transition time in a two-state scattering problem. The exact analytical expression for the time of transition $tau$ is derived.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $V_{12}=V_{21}=k_0 \delta(x)$. The exact analytical expression for the time of transition $\tau$ is derived. We notice $\tau$ 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 $\tau$ 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.

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