In quantum mechanics, the position operator(for a single particle moving in one dimension) is defined as [itex] Q(\psi)(x)=x\psi(x) [/itex], with the domain [itex] D(Q)=\{\psi \epsilon L^2(\mathbb R) | Q\psi\epsilon L^2 (\mathbb R) \} [/itex]. But this means no square-integrable function in the domain becomes non-square-integrable after being acted by this operator which, in turn, means there exist no function in the domain for which you can't have a M that satisfies [itex] ||Q \psi|| \leq M ||\psi|| [/itex] and so this operator should be bounded. But people say its not bounded!(adsbygoogle = window.adsbygoogle || []).push({});

I'm really confused. What's the point here?

Thanks

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# Confusion about position operator in QM

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