Let us say that I apply a non-unitary transformation \def\ket#1{| #1\rangle} \def\braket#1#2{\langle #1|#2\rangle} \hat A to the ket's: \ket{\psi} \rightarrow \hat A \ket{\psi} \ket{\phi}\rightarrow \hat A \ket{\phi} Clearly in this case the probability: P=|\braket{\phi}{\psi}|^2 Will change. What physically is going on here? i.e. why for unitary operators we can perform such a transformation but for non-unitary operators we can't?
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