I want to ask how to deal with the equation on $L/2 < x < L$ region.
The equation has a general form $C e^{-k_2 L/2} + D e^{k_2 L/2}$ on $L/2 < x < L$.
However, as there exists infinite barrier at $x = L$, we do have non-zero $D$.
Then the boundary condition at $x = L/2$ yields
$B e^{i k_1 L / 2} = C e^{-k_2 L/2} + D e^{k_2 L/2}$ ... (1)
and
$i k_1 B e^{i k_1 L / 2} = k_2( - C e^{-k_2 L/2} + D e^{k_2 L/2})$ ... (2)
However, dividing (1) with (2) would not cancel the RHS terms that we usually see in quantum physics textbooks.
Is there anyway to solve the Schrodinger equation in this setting?