I am rather confused because it would seem that mathematical conclusions I have drawn here goes against my physical intuition, though both aren't too reliable to begin with.
We have a potential step described by $$V(x)=\begin{cases}0& x\le0\\V_0 & x>0\end{cases}$$
and a wavefunction $\psi(x)$ that satisfies the equation $${\hbar^2\over 2m}{\partial^2 \over \partial x^2}\psi(x)+V(x)\psi(x)=E\psi(x).$$
I wish to find the probability of reflection. By continuity constraints at $x=0$ I have arrived at the reflection amplitude being $$R={k-q\over k+q},$$ where $k=\sqrt{2mE\over \hbar^2}$ and $q=\sqrt{2m(E-V_0)\over \hbar^2}$ then we let $V_0\to -\infty$ giving $q\to \infty$, so $R\to -1$
$\implies |R|^2\to 1.$
But I would have guessed that $|R|^2$ should vanish at the limit so that the incident wave is totally transmitted!
Could someone please explain?