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PHI(left) = Aexp(ikx)+Bexp(-ikx)

PHI(right) = Cexp(-qx)

Continuity of the function and it's derivative at x=0 gives the relations between the parameters A, B and C.

Solving the appropriate equations we obtain

R = |B\A|^2 = 1

meaning that there is total reflection; hence the transmission must be zero.

But if we calculate the probability of finding a particle, say in the interval a<x<2a, we get a non-zero probability (because PHI(right) does not venish).

How is it possible, if every particle must be reflected?