Operators interpretation (Dirac notation)

[rsaad]

Hi all!
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!

 

[Fredrik]

Interpret what exactly? The operator, the equality you posted, or just the right-hand side of that equality? To fully define the operator, you must specify its action on all members of an orthonormal basis, not just its action on one of them. I don't see a way to interpret the equality. To interpret the state, you must explain what |1> and |2> are.