Can you give a more exact reference? A link to the exact page at google books would be the best way to reference it.
I assume it has something to do with the common claim that square integrable functions must go to zero as the variable goes to infinity ([itex]\psi(x)\rightarrow 0[/itex] when [itex]x\rightarrow\infty[/itex]), which is actually wrong. (There are counterexamples. See this thread). However, I think [itex]\psi(x)[/itex] must go to zero as x goes to infinity if [itex]Q\psi[/itex] (where Q is the position operator) is square integrable. Maybe it also has to go to zero if [itex]P\psi[/itex] (where P is the momentum operator) is square integrable? (I don't have time to think that through right now).
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