# Dirac Delta Potential and bound/scattered states

Why does the attractive Dirac Delta distribution (function) potential $V = \alpha\delta$(x) (for negative $\alpha$) yield both bound AND scattered states? Is this due to the definition of the Dirac delta distribution? Or is it for a different reason?

• What sort of answer beyond "well, because these solutions to the energy eigenvalue problem (aka Shrodinger equation) exist" are you looking for? Perhaps it's physical intuition you're after? – joshphysics Aug 6 '13 at 20:11
• Is there a finite potential which doesn't yield scattered states? – ZachMcDargh Aug 6 '13 at 20:49
• In re Zach's comment, Weston showed in 63 a wide range of scattering bodies in which there is zero backscattered field. Then it was a curiosity but now with metamaterials you can do some really crazy stuff. The DOI for Weston's paper is 10.1109/TAP.1963.1138082 – user27777 Aug 6 '13 at 22:46