A question is given in Griffiths. Consider the "step" potential V(x) which rises to Vo (at x=0) which is 0 for x<0. For the scattering states and E less than Vo, the reflection coefficient comes out to be 1. It means that the particle can't cross the barrier from the left-hand side.
Doesn't scattering state mean that the particle can cross every (finite) barrier with some non-zero probability? If not, then what is meant by a scattering state?
I want to state humbly that I'm not asking the definition of scattering state on the basis of potential at infinity.