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If you are given an operator such that A|1> = √(1/3) |1> +√(2/3) |2>, how do we interpret it?

I do know that 1/3 and 2/3 are probabilities but is this operator application on state one suggesting that this state in state 1 and 2 with probabilities 1/3 and /3 respectively?

Thank you!

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# Operators interpretation (Dirac notation)

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