All Problems Wave Properties of particles. Schrodinger Equation.
Problem 6.95
Employing Eq. \((6.2 \mathrm{e}),\) find the probability \(D\) of an electron with energy \(E\) tunnelling through a potential barrier of width \(l\) and height \(U_{0}\) provided the barrier is shaped as shown: (a) in Fig. 6.4 (b) in Fig. 6.5 .
6.95. (a) \(D \approx \exp \left[-\frac{2 l}{\hbar} \sqrt{2 m\left(U_{0}-E\right)}\right]\) (b) \(D \approx \exp \left[-\frac{8 l \sqrt{2 m}}{3 \hbar U_{0}}\left(U_{0}-E\right)^{3 / 2}\right]\)