QM-22 WKB Approximation

[1]  Plot the potential

\begin{equation} V(x) = \begin{cases} 0 & \text{for } x < 0\\ V_0 -f x & \text{for } x \ge 0 \end{cases} \end{equation}

and find the transmission coefficient for the potential barrier using WKB approximation for $E=3V_0/4$.

[2] Find the transmission probability that an alpha particle with energy  $E= Ze^2/ 4R$  will come out of a  a nucleus of charge $Z$ and radius $R$. You may assume that the potential seen by the  alpha particle inside the nucleus can be represented by a square well of range $R$.

Suggested Reference

The transmission coefficient through an inverted parabolic barrier        $$ V(x) = - \frac{1}{2} k x^2 $$ can be computed exactly by first finding the asymptotic from of the wave function.

See Landau and Lifshitz, "Quantum Mechanics''.