Does a Delta Potential Barrier Allow for Bound Solutions?

[dyn]

Hi.
I understand that in 1-D when E< V(minimum) there exist no physically acceptable solution to the Schrödinger Equation. I have been looking at delta potentials using Griffiths book. I follow his working for the delta potential well but when it comes to the potential barrier I don't understand where the mathematics shows that no bound solutions exist for the delta barrier. If anyone has this book can they point out the step at which the maths for the well shows that the barrier has no bound solutions ?

 

[DrClaude]

The condition for a bound state is given by eps. [2.109]. In the case of a potential barrier (not necessarily a delta potential), a bound state would correspond to a solution where $E < V(x) \forall x$. This is the same problem as for a free particle ($V(x) = 0$), and no acceptable solution exists for $E \leq 0$, see footnote 34 on page 69.