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Jul 13, 2021 at 5:58 comment added Carlo Beenakker there is no need to assume that $\lambda_n$ is distinct from a $\lambda$ in the continuous spectrum -- states which are localized in space at an energy that falls in the continuum band do exist.
Jul 13, 2021 at 4:57 comment added mathamphetamine See this: en.m.wikipedia.org/wiki/Bound_state_in_the_continuum
Jul 13, 2021 at 4:52 comment added mathamphetamine @williewong : does this also rule out bound states for values of $\lambda$ in the continous spectrum?
Jul 13, 2021 at 3:53 comment added Willie Wong In other words, the equivalence the OP asked about is extremely generic.... because it is by definition.
Jul 12, 2021 at 20:31 history answered Carlo Beenakker CC BY-SA 4.0