Let H be a hilbert space and let ˆA be a linear operator on H.
My textbook states that |ˆAψ⟩=ˆA|ψ⟩. My understanding of bra-kets is that |ψ⟩ is a member of H and that ψ alone isn't defined to be anything, so |ˆAψ⟩ isn't defined.
Is |ˆAψ⟩=ˆA|ψ⟩ just a notation or is there something deeper that I am missing?
Answer
This should be understood as a mere definition, i.e. a new label for the state you get when you apply the operator A to the ket psi.
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