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 Quote by Identity I'm not sure if you understood what I meant, sorry The general solution is of the form: $$\psi(x) = \begin{cases} Ae^{ik_1x}+A\frac{k_1-k_2}{k_1+k_2}e^{-ik_1x} \ \ \ \ \ \ x < 0\\\\ A\frac{2k_1}{k_1+k_2}e^{ik_2x}\ \ \ \ \ \ x \geq 0\end{cases}$$ Hence, $$|\psi(x)|^2 = \begin{cases} A^2\left[1+\left(\frac{k_1-k_2}{k_1+k_2}\right)^2+2\frac{k_1-k_2}{k_1+k_2}\cos{2k_1x}\right] \ \ \ \ \ \ x < 0 \\\\ A^2\frac{4k_1^2}{(k_1+k_2)^2}\ \ \ \ \ \ x \geq 0\end{cases}$$ For $$x<0$$ we have a cosine wave which can't be normalised, since it has a vertical translation For $$x>0$$ we have a constant, which is certainly not normalisable. The are continuous and differentiable at $$x=0$$, and in all regions satisfy the schrodinger equation for the potential step However, since they are NOT normalisable, how do you interpret them?