Abstract
The inverted parabola remains an exactly solvable tunneling barrier when imaginary parts are added to the potential. They represent the effect of particle absorption. In the limit of strong absorption (“opaque barrier”) convenient limiting forms for the tunneling probability are derived using asymptotic expansions of the exact scattering solution. An application to Zener tunneling is made and the result is compared to the case of tunneling under viscous dissipation. Significant differences are found between these two approaches to tunneling under dissipation.
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