I was looking at solved example (3.13) in the Schaum's Series book on QM by Yoav Peleg et al (2nd edn), where they solve for a step potential where a high energy particle is coming from the left and going right (the step potential's rise being from left to right). In the explanation, the author says that
"since the particle is known to go from left to right, hence we can omit the left-travelling wave in the high potential (right side) region)".
I am uncomfortable with this kind of justification, my discomfort originating from the fact that in QM I have seen that sometimes we resort to intuitive analogues as in the above example, but sometimes we don't and we're encouraged not to because QM is often counter-intuitive (eg. in a periodic crystal, the momentum of the Bloch electron is different from the crystal momentum $\hbar k$
Is there a better or a more formal justification for the above example as regards why we omit the left travelling wave in the high potential region?