Smooth double barriers in quantum mechanics
Avik Dutt, Sayan Kar (IIT Kharagpur, India)
TL;DR
This paper analyzes quantum tunneling through smooth double barriers modeled with Gaussian functions, exploring transmission probabilities, resonances, and tunneling times using numerical and WKB methods.
Contribution
It provides a detailed comparison of numerical and WKB approaches for smooth Gaussian barriers, extending known results for rectangular barriers to more realistic potentials.
Findings
Transmission probabilities and resonances depend on barrier parameters.
Generalized tunneling time expressions for smooth barriers.
Numerical and WKB results show good agreement.
Abstract
Quantum mechanical tunneling across smooth double barrier potentials modeled using Gaussian functions, is analyzed numerically and by using the WKB approximation. The transmission probability, resonances as a function of incident particle energy, and their dependence on the barrier parameters are obtained for various cases. We also discuss the tunneling time, for which we obtain generalizations of the known results for rectangular barriers.
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