I got a question which I'm quite stuck on...
Given the eigenvalue problem,
Show that if is an eigenvalue, then must have a specific value and find this value. If , show that there is exactly one negative eigenvalue.
I believe I've done the first part, as my working is as follows:
Rearrange the HLDE into self adjoint form: , and taking that , means the HLDE becomes . The general solution to this should be of the form . Using the boundary conditions,
Does this look correct?
The next part of the question I get stuck on. The general solution for is .
Using the boundary conditions
From here, I not sure where to go... have I do the right thing?
Thanks for your time.