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arXiv · 1504.00115

New shape resonances in one dimension

Zafar Ahmed·Shashin Pavaskar·Lakshmi Prakash
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Abstract

Hitherto, a finitely thick barrier next to a well or a rigid wall has been considered the potential of simplest shape giving rise to resonances (metastable states) in one dimension: $x \in(-\infty, \infty)$. In such a potential, there are three real turning points at an energy below the barrier. Resonances are Gamow's (time-wise) decaying states with discrete complex energies $({\cal E}_n = E_n -iΓ_n/2)$. These are also spatially catastrophic states that manifest as peaks/wiggles in Wigner's reflection time-delay at $E = ε_n \approx E_n$. Here we explore potentials with simpler shapes giving rise to resonances - two-piece rising potentials having just one-turning point. We demonstrate our point by using rising exponential profile in various ways.

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Zafar Ahmed, Shashin Pavaskar, Lakshmi Prakash. 2015-05-25. New shape resonances in one dimension. https://doi.org/10.1088/0143-0807%2F36%2F4%2F048001

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