I need some help with a homework problem... solving for the l=0 bound states (E<0) of the spherical delta function potential.

V(r)=-Aδ(r-a), where r is the distance from the origin, A is a constant, the shell is of radius a.

So far I plugged this into the radial equation, and I'm confused with how to solve from here. I know that you have to consider the regions r<a and r>a separately, and then apply BCs for continuity. My question is, what should I take for my "k" values? When r does not equal a, V(r)=0 and the solutions for r<a are the same as r>a if we set

k=√(-2mE)/h^2, where h=h bar

Notice I put the negative sign under the square root because for bound states E<0.

I know I'm missing something here... Willing to tell you more about my method of solving if this effort seems unsatisfactory. Just too lazy to type up all the math symbols.

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