On the problem of quantum tunneling of a singular potential

Abstract

The problem of quantum tunneling through the singular potential barrier \(V(x) = \left\{ {\begin{array}{*{20}c}
{V_0 (b/x - x/a)^2 ,} & {0 < \left| x \right| \leqslant \sqrt {ab} } \\
{0,} & {\left| x \right| > \sqrt {ab} } \\

\end{array} } \right.\) is discussed on the subject of the possibility to replace the singular behavior of the problem at the point x = 0 by a limiting process at the top of the truncated potential. The validity of such a replacement and, on this basis, the zero transparency of the quantum potential barrier are shown.