Special rectangular (double-well and hole) potentials

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{ö}dinger equation as $\psi (x)=Bx+C$.

arXiv comment15 pages, seven figures and 2 Tables

Cited by in corpus (1)

• Avoided crossings of energy levels in one-dimension