Problem 6.94

Particles of mass $m$ and energy $E$ move from the left to the potential barrier shown in Fig. 6.3. Find: (a) the reflection coefficient $R$ of the barrier for $E>U_{0}$; (b) the effective penetration depth of the particles into the region $x>0$ for $E< U_{0},$ i.e. the distance from the barrier boundary to the point at which the probability of finding a particle decreases e-fold.