Consider I have the following commutator, $[H,O]$ where $O$ is some hermitian operator.
I know that if $$H|\psi\rangle=E|\psi\rangle$$
Where $|\psi\rangle$ represents the bound energy eigenkets, for example the bound states for the Hydrogen atom. In this case, I know:
$$\langle\psi|[H,O]|\psi\rangle=0$$
However, consider now that I have scattering states, again considering the continuous energy eigenstates of the hydrogen atom. Does the above equation still hold true in this case ?
Are expectation values for any hermitian operator, well defined in case of scattering states, or rather non-normalizable states ?
