# Confusion about the reflection coefficient when a particle going through a potential

Suppose we have a potential$$V(x) = \begin{cases} 0, & \text{if  x \le 0} \\ V_0 & \text{if  x \gt 0 } \end{cases}$$ The reflection coefficient for the case $E \lt V_0$ is $1$, which means all the waves are reflected back.

But I've got a question: we know from the calculation, there is some waves which can pass through the barrier, though decaying exponentially, then how is the reflection coefficient be $1$. Does that mean the waves which pass through the barrier will eventually reflect back?

From the definition of the reflection and transmission coefficients, for the case $E<V$, $R=1$ means that there is NO CURRENT, or NO FLUX of particles at all. You can find particles behind the potential step: yes, it's true. But it does not mean that you can find a FLUX of particles. So, it is ok here.
Second, unless I'm grossly mistaken, the reflection coefficient at a step potential is not 1.0, even for the case that $E < V_{0}$.