[UPSC CSE 2008] Schrodinger’s Wave equation and applications (Q205, 30M)

Show that the probability of transmission across the step barrier represented by the potential V(x) = \begin{cases} 0 & \text{for } x < 0 \\ V_0 & \text{for } x > 0 \end{cases} is T = \frac{4 k_1 k_2}{(k_1 + k_2)^2}, where k_1 and k_2 are wave numbers in regions x < 0 and x > 0, respectively.