A quantum mechanical particle of mass $m$ and energy $E$ encounters a potential step,

$$V(x)= \begin{cases}0, & x<0 \\ V_{0}, & x \geqslant 0\end{cases}$$

Calculate the probability $P$ that the particle is reflected in the case $E>V_{0}$.

If $V_{0}$ is positive, what is the limiting value of $P$ when $E$ tends to $V_{0}$ ? If $V_{0}$ is negative, what is the limiting value of $P$ as $V_{0}$ tends to $-\infty$ for fixed $E$ ?