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arXiv · 1401.8070

Special rectangular (double-well and hole) potentials

Zafar Ahmed·Tanayveer Bhatia·Shashin Pavaskar·Achint Kumar
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Abstract

We revisit a rectangular barrier as well as a rectangular well (pit) between two rigid walls. The former is the well known double-well potential and the latter is a hole potential. Let $|V_0|$ be the height (depth) of the barrier (well) then for a fixed geometry of the potential, we show that in the double-well, $E=V_0(>0)$, and in the hole potential ($V_0 <0$), $E=0$, can be energy eigenvalues provided $V_0$ admits some special discrete values. These states have been missed out earlier which emerge only when one seeks the special zero-energy solution of one-dimensional Schr{\"o}dinger equation as $\psi(x)=Bx+C$.

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Zafar Ahmed, Tanayveer Bhatia, Shashin Pavaskar, Achint Kumar. 2014-01-31. Special rectangular (double-well and hole) potentials. https://arxiv.org/abs/1401.8070

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