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Then we have solution on both sides of boundary in the form of wave functions....

Is the reflection coefficient in this case simply (E-V)/E ??

Can anyone show me a more formal explanation, however not as formal as in books (so that i understand :)

What does the quantum mechanical coefficient really tell us (in comparison with classical thinking)?

If we think about it classically I think we can be sure that particle gets transmitted at boundary, but loses some energy.

From the QM point of view, on the other hand I guess we have a probability that particle gets reflected?

Please tell me if my reasoning is correct:) cheers!