Delta well + infinite barrier -> bound state

[maverick280857]

Think of the delta function, with positive lambda, as a very narrow, deep potential well. Use your common sense and experience with the potential well to get the appropriate general form of the solution.
Regards,
Reilly Atkinson

Reilly, thanks for your reply, but which part are you referring to?

As I stated in an earlier post, I was able to get the bound state solution. But in post #18, I posed the second part of the problem, which deals with the asymptotic nature of the wavefunction in case of a scattering problem for the same V(x). I solved that and got an equation for the phase shift.

But as far as I can tell, the phase shift can be determined exactly from that equation and unless I have made a mistake in the computation, there is no need to assume that $\phi \approx ak$ and determine $a$ as the question demands.