Delta potential boundary conditions for E>0 scattering states

[atomqwerty]

Just a quick question

A delta Potential is given by -Vδ(x-a). If we wrote the equations of the wave function like this

For E>0

u(x) = Aexp(ikx) + A'exp(-ikx) for x<a
u(x) = Bexp(ikx) + B'exp(-ikx) for x>a

do i have to impose that A'=B=0 in order to u(x) not diverge in when x goes to +-infinite?

The problem is that where I read that, only impose the condition for E<0.

Thanks!

 

[sgd37]

but u(x) doesn't diverge at all since exp(+/-ikx) = cos(kx)+/-isin(kx) and this is the unit circle in the C plane. The only boundary condition is that u(a)=u'(a) for x <a , x>a respectivley