4. [9 points] Consider a potential step given by:
$U(x) = \begin{cases} 0, & x < 0 \\ U_0, & x > 0 \end{cases}$
with $E > U_0$. The general solution to the Schrödinger in each of these regions is given by:
$\psi(x) = \begin{cases} A'e^{ik_0x} + B'e^{-ik_0x}, & x < 0 \\ C'e^{ik_1x} + D'e^{-ik_1x}, & x > 0 \end{cases}$
Apply the continuity conditions on $\psi$ and $\frac{d\psi}{dx}$ to find $B'$ and $C'$ in terms of $A'$, assuming particles
are incident from the negative $x$ direction. Evaluate the reflection and transmission coefficients
$R = \frac{|B'|^2}{|A'|^2}$ and $T = \frac{k_1|C'|^2}{k_0|A'|^2}$, and calculate the sum $R + T$. Assume $k_0 = 42$ and $k_1 = 14.$
