On page 2 of the above pdf they describe how they select their wavefunctions. Finding the general solution is easy but they then go on to say that D= 0 because 'this is not physically meaningful' leaving $\psi=Ce^{ik_2x}$.
Fine, I can see that if the wave is transmitted through the barrier it is best represented by such a travelling wave moving in the +x direction.
Now, my lecturer also supports and uses the above explanation.
However, there are a few university websites and a textbook (Introduction to Quantum Mechanics by Bransden) that state that the wavefunction for the section $V(x) = V_0$ cannot be represented by $\psi=Ce^{ik_2x}$ as this tends to infinity at x= infinity. Also, by the postulates of QM the wavefunction must have a real quantifiable integral which such a function is in violation of.
What do I follow ? Who is right ?