If we have an operator A which operates on some state described by vector x the result is a new vector y(adsbygoogle = window.adsbygoogle || []).push({});

A |x> = |y>

My question is: is the new vector y considered to be a different state vector in the same vector space as x or is it considered to be a vector in an entirely different vector space? If the former then what does that new vector represent (I would assume a new state of the system after the operator)? If the latter then what does that new vector space represent?

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# Resulting state vector interpretation

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