Evanescent wave / tunneling

[jaejoon89]

How is the wavefunction within a rectangular potential barrier an evanescent wave?

I thought an evanescent wave was exponentially decaying. If you take x->infinity for the following function for E<V, one of the terms goes to 0 but the other term goes to infinity, so the wavefunction will go to infinity. Thus, it isn't physically realizable. But how you get the physically realizable wavefunction for E<V, what does it look like, and how is it an evanescent wave?

http://en.wikipedia.org/wiki/Schrödinger_equation#Time_independent_equation

 

[NateD]

_in_one_dimensionThe wavefunction within a rectangular potential barrier is an evanescent wave because the wavefunction decays exponentially away from the barrier. This behavior can be seen in the solution to the Schrödinger equation for a one-dimensional energy-independent potential, which has two components: a propagating wave and an exponentially decaying evanescent wave. For energies less than the potential barrier, only the decaying evanescent wave is present. This means that the wavefunction is exponentially decreasing away from the barrier.