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Nov 4 at 1:07 comment added naturallyInconsistent You are getting confused over something insane. Consider a free particle. Then the momentum eigenstate is also a stationary state. It simply is the case that input and output are still well-defined when considering stationary states.
Nov 3 at 18:09 comment added Neel Thank you! Just to be clear, the correct criteria that you are referring to is $B''=0$, right? I am still however, a little bit confused. Even if we do assume $B'' = 0$, we still have solved for a stationary state of the system that gives the probability density of finding the particle in a particular place at a single instant of time. We don't actually follow the process of scattering, starting from the particle moving toward the wall and then checking whether transmission occurred? Why are these two processes the same?
Nov 3 at 18:04 vote accept Neel
Nov 3 at 18:07
Nov 3 at 9:54 history answered naturallyInconsistent CC BY-SA 4.0