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I've found the following relation (in a book about the qm 3-body scattering theory):

[tex]<\Omega^{\pm}^{\dagger} \Psi_n|p>= ... = 0[/tex]

where [tex]|p>[/tex] is a momentum eigenstate.

So it is shown, that the inner Product is zero. Then they conclude that [tex]\Omega^{\pm}^{\dagger}|\Psi_n> = 0[/tex] because the p-states form a complete set.

How can this formally be shown?

thanky you.