Wave Function for Delta Function Barrier with E<0

[Seriously]

Given a delta function barrier located at x=0: V(x) = +a * delta(x)
If you have a particle incident from the left with E<0, what does the wave function look like??

I have trouble with this because I thought the particle energy needed to be greater than the minimum potential (E > Vmin) for you to get a solution.

I figure there are no bound states (only scattered states). But what does that mean for the wave function with E<0?

 

[kcirick]

If E < V, you will get a tunelling effect (one of those things I will have to learn myself), but I think basically when you come out from the other end of the barrier, the energy of the wave is lower than the original wave. I'm not sure what the wave function $\Psi$ will look like though...

 

[quasar987]

But here, Vmin=0!

In a usual potential step or potential barrier problem, E>Vmin, and the wave function inside the barier or walls is an atenuation of where E>V. Here however, E<V everywhere! So my intuition tells me that psi would be 0 everywhere in this situation.

Could it be that there is an error in the question? That it E>0 was meant rather than E<0?

 

[Seriously]

Exactly! Vmin=0... and therefore E<0 always gives E<Vmin. So I don't understand.

I double checked the question. It specifically states E<0. It then asks if there are any bound states (answer=no), and wants me to draw the wave function.

I was told that E<0 just means that the energy is less than the minimum potential energy which can be drawn anywhere. But this makes no sense to me.