Is there any case of potential $V$, such that the continuity of the operator $H=c\ \Delta+V$ is not spoiled?
And I don't know any non-differnetial operator examples for continous spectra. I guess I don't know the full spectrum of operators (ba dum tss!).
My question comes about as I wonder about the justification of the term "bounded state", especially in relatoion to the fairly straight forward classical concept.