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.