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Jul 19, 2023 at 8:13 vote accept Rasmus Andersen
Jul 19, 2023 at 8:13 comment added Rasmus Andersen Okay, thank you. This clears up some of the confusion, but I will sit down and study the details at a later point.
Jul 18, 2023 at 11:14 comment added Roger V. @RasmusAndersen see also the remark that I added to the answer.
Jul 18, 2023 at 11:14 history edited Roger V. CC BY-SA 4.0
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Jul 18, 2023 at 10:59 comment added Roger V. @RasmusAndersen term $Fe^{iqx}$ corresponds to the current flowing to the right, whereas term $G^{-iqx}$ is the current flowing to the left - you can easily calculate the current for a plane wave using usual prescription. The solution in the OP is for the (incoming) wave incident from the left. If you consider a wave incident from the right or if you decide to work with outgoing waves, you will have $G^{-iqx}$.
Jul 18, 2023 at 10:25 comment added Rasmus Andersen Okay, thank you for the good links you provided. I understand that we can determine the two solutions to TISE by for instance considering the wave flux propagating from left-to-right (in this problem specifically). Now, if we do consider this derivation-method for the two solutions, I still cannot see how the term $G\text{e}^{-iqx}$ is discarded. Although the links you provided give good insight, I am not quite sure how they answer this question in particular.
Jul 18, 2023 at 9:55 history answered Roger V. CC BY-SA 4.0